Heat & Thermodynamics
Q. A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. Assuming no heat loss to the surroundings, what is the final temperature of the system? (Specific heat of water = 4.18 kJ/kg°C, specific heat of metal = 0.9 kJ/kg°C) (2020)
A.
25°C
B.
30°C
C.
35°C
D.
40°C
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Solution
Using the principle of conservation of energy, set heat lost by metal equal to heat gained by water to find the final temperature.
Correct Answer: C — 35°C
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Q. A 100 g piece of metal at 100°C is placed in 200 g of water at 20°C. What will be the final temperature of the system? (Specific heat of water = 4.2 J/g°C, specific heat of metal = 0.5 J/g°C) (2023)
A.
30°C
B.
40°C
C.
50°C
D.
60°C
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Solution
Using the heat transfer equation, we can find the final temperature to be 50°C.
Correct Answer: C — 50°C
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Q. A 2 kg block of ice at 0°C is converted to water at 0°C. How much heat is absorbed if the latent heat of fusion of ice is 334,000 J/kg?
A.
668,000 J
B.
334,000 J
C.
167,000 J
D.
500,000 J
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Solution
Heat absorbed = mass * latent heat = 2 kg * 334,000 J/kg = 668,000 J.
Correct Answer: A — 668,000 J
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Q. A 2 kg block of metal at 100°C is placed in 1 kg of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.2 J/g°C, specific heat of metal = 0.9 J/g°C) (2021)
A.
30°C
B.
40°C
C.
50°C
D.
60°C
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Solution
Using the heat transfer equation, the final temperature can be calculated to be 50°C.
Correct Answer: C — 50°C
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Q. A 5 kg block of ice at 0°C is converted to water at 0°C. If the latent heat of fusion of ice is 334 kJ/kg, how much heat is absorbed?
A.
1670 kJ
B.
334 kJ
C.
167 kJ
D.
3340 kJ
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Solution
Heat absorbed (Q) = m * Lf = 5 kg * 334 kJ/kg = 1670 kJ.
Correct Answer: B — 334 kJ
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Q. A gas expands from 2 L to 5 L at a constant pressure of 1 atm. How much work is done by the gas? (2023)
A.
3 L·atm
B.
5 L·atm
C.
2 L·atm
D.
1 L·atm
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Solution
Work done by the gas during expansion at constant pressure is W = PΔV. Here, ΔV = 5 L - 2 L = 3 L, so W = 1 atm * 3 L = 3 L·atm.
Correct Answer: A — 3 L·atm
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Q. A gas expands isothermally at 300 K and absorbs 600 J of heat. What is the work done by the gas? (2023)
A.
600 J
B.
300 J
C.
900 J
D.
0 J
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Solution
In an isothermal process, the work done by the gas is equal to the heat absorbed. Therefore, work done = 600 J.
Correct Answer: A — 600 J
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Q. A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressure of the gas is 100 kPa, what is the work done by the gas? (2020)
A.
0 kJ
B.
10 kJ
C.
20 kJ
D.
30 kJ
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Solution
Work done (W) = P * ΔV = 100 kPa * (2 m³ - 1 m³) = 100 kPa * 1 m³ = 100 kJ = 10 kJ.
Correct Answer: B — 10 kJ
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Q. A gas is compressed isothermally from a volume of 4 L to 1 L at a constant temperature of 300 K. If the initial pressure is 1 atm, what is the final pressure?
A.
4 atm
B.
3 atm
C.
2 atm
D.
1 atm
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Solution
Using Boyle's Law, P1V1 = P2V2, we find P2 = P1 * (V1/V2) = 1 atm * (4 L / 1 L) = 4 atm.
Correct Answer: A — 4 atm
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Q. How much heat is required to raise the temperature of 250 g of water from 25°C to 75°C? (Specific heat of water = 4.2 J/g°C) (2020)
A.
5250 J
B.
4200 J
C.
2500 J
D.
1000 J
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Solution
Heat required = mass × specific heat × change in temperature = 250 g × 4.2 J/g°C × (75°C - 25°C) = 5250 J.
Correct Answer: A — 5250 J
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Q. How much heat is required to raise the temperature of 500 g of water from 25°C to 75°C? (2020)
A.
10000 J
B.
5000 J
C.
20000 J
D.
15000 J
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Solution
Q = mcΔT = 500 g * 4.2 J/g°C * (75 - 25)°C = 10000 J.
Correct Answer: D — 15000 J
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Q. If 1 kg of water is heated from 25°C to 75°C, how much heat is absorbed? (Specific heat of water = 4.2 J/g°C) (2021)
A.
21000 J
B.
42000 J
C.
84000 J
D.
105000 J
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Solution
Q = mcΔT = (1000 g)(4.2 J/g°C)(50°C) = 210000 J.
Correct Answer: B — 42000 J
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Q. If 1000 J of heat is added to a gas and it expands doing 400 J of work, what is the change in internal energy? (2023)
A.
600 J
B.
400 J
C.
1000 J
D.
200 J
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Solution
Using the first law of thermodynamics: ΔU = Q - W = 1000 J - 400 J = 600 J.
Correct Answer: A — 600 J
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Q. If 1000 J of heat is added to a system and it does 400 J of work, what is the change in internal energy? (2021)
A.
600 J
B.
400 J
C.
1000 J
D.
1400 J
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Solution
Using the first law of thermodynamics, ΔU = Q - W = 1000 J - 400 J = 600 J.
Correct Answer: A — 600 J
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Q. If 200 g of water at 80°C is mixed with 300 g of water at 20°C, what will be the final temperature of the mixture? (Assume no heat loss to the surroundings)
A.
30°C
B.
40°C
C.
50°C
D.
60°C
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Solution
Using the formula m1c1T1 + m2c2T2 = (m1 + m2)cTfinal, we find Tfinal = 40°C.
Correct Answer: B — 40°C
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Q. If 500 J of heat is added to a system and 200 J of work is done by the system, what is the change in internal energy of the system?
A.
300 J
B.
500 J
C.
700 J
D.
200 J
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Solution
According to the first law of thermodynamics, ΔU = Q - W. Here, ΔU = 500 J - 200 J = 300 J.
Correct Answer: A — 300 J
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Q. If 500 J of heat is added to a system and it does 200 J of work, what is the change in internal energy? (2022)
A.
300 J
B.
200 J
C.
500 J
D.
700 J
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Solution
According to the first law of thermodynamics, ΔU = Q - W. Here, ΔU = 500 J - 200 J = 300 J.
Correct Answer: A — 300 J
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Q. If the latent heat of fusion of ice is 334 J/g, how much heat is required to melt 50 g of ice? (2019)
A.
1670 J
B.
3340 J
C.
5000 J
D.
1000 J
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Solution
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
Correct Answer: A — 1670 J
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Q. If the volume of a gas is doubled at constant temperature, what happens to its pressure?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
According to Boyle's Law, at constant temperature, pressure is inversely proportional to volume. Therefore, if the volume is doubled, the pressure is halved.
Correct Answer: B — It halves
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Q. If the volume of a gas is halved while keeping the temperature constant, what happens to the pressure of the gas?
A.
Halves
B.
Doubles
C.
Remains the same
D.
Increases by 50%
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Solution
According to Boyle's Law, if the volume is halved, the pressure doubles.
Correct Answer: B — Doubles
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Q. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)
A.
40%
B.
50%
C.
60%
D.
70%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: C — 60%
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Q. In an adiabatic process, the temperature of an ideal gas decreases. What happens to its pressure?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Depends on volume
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Solution
In an adiabatic process, as the temperature decreases, the pressure also decreases due to the ideal gas law.
Correct Answer: B — Decreases
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Q. What is the change in internal energy of a system if 200 J of heat is added and 50 J of work is done by the system?
A.
150 J
B.
250 J
C.
200 J
D.
100 J
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Solution
Using the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.
Correct Answer: A — 150 J
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Q. What is the change in internal energy of a system if 300 J of heat is added and 100 J of work is done by the system? (2021)
A.
200 J
B.
300 J
C.
400 J
D.
500 J
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Solution
Using the first law of thermodynamics: ΔU = Q - W = 300 J - 100 J = 200 J.
Correct Answer: A — 200 J
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Q. What is the efficiency of a Carnot engine operating between 300 K and 600 K? (2022)
A.
0.5
B.
0.33
C.
0.25
D.
0.67
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Solution
Efficiency = 1 - (T_c/T_h) = 1 - (300/600) = 0.5.
Correct Answer: A — 0.5
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Q. What is the efficiency of a Carnot engine operating between 500 K and 300 K? (2022)
A.
0.4
B.
0.5
C.
0.6
D.
0.7
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Solution
Efficiency = 1 - (T2/T1) = 1 - (300/500) = 0.4 or 40%.
Correct Answer: C — 0.6
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Q. What is the efficiency of a Carnot engine operating between a hot reservoir at 600 K and a cold reservoir at 300 K?
A.
0.5
B.
0.33
C.
0.25
D.
0.75
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Solution
Efficiency (η) = 1 - (T_c/T_h) = 1 - (300/600) = 0.5 or 50%.
Correct Answer: B — 0.33
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Q. What is the efficiency of a Carnot engine operating between temperatures of 500 K and 300 K?
A.
0.4
B.
0.5
C.
0.6
D.
0.7
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Solution
Efficiency (η) = 1 - (T2/T1) = 1 - (300/500) = 0.4 or 40%.
Correct Answer: C — 0.6
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Q. What is the final temperature when 200 g of ice at 0°C is added to 100 g of water at 80°C? (Specific heat of water = 4.2 J/g°C) (2020)
A.
0°C
B.
20°C
C.
40°C
D.
80°C
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Solution
Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. Solving gives a final temperature of 20°C.
Correct Answer: B — 20°C
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Q. What is the final temperature when 200 g of ice at 0°C is added to 100 g of water at 80°C? (Assume no heat loss to the surroundings) (2023)
A.
0°C
B.
20°C
C.
40°C
D.
80°C
Show solution
Solution
Using heat balance: m_ice * L_f + m_water * c * (T_final - 80) = 0. Solving gives T_final = 20°C.
Correct Answer: B — 20°C
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