What is the change in internal energy of 1 mole of an ideal gas when it is heate
Practice Questions
Q1
What is the change in internal energy of 1 mole of an ideal gas when it is heated at constant volume from 300 K to 600 K?
0 J
300 J
600 J
900 J
Questions & Step-by-Step Solutions
What is the change in internal energy of 1 mole of an ideal gas when it is heated at constant volume from 300 K to 600 K?
Step 1: Identify the formula for the change in internal energy (ΔU) of an ideal gas at constant volume: ΔU = n * Cv * ΔT.
Step 2: Determine the number of moles (n). In this case, n = 1 mole.
Step 3: Find the specific heat at constant volume (Cv) for a monatomic ideal gas. For a monatomic gas, Cv = (3/2)R, where R is the ideal gas constant (8.31 J/mol K).
Step 4: Calculate Cv: Cv = (3/2) * 8.31 J/mol K = 12.465 J/mol K.
Step 5: Calculate the change in temperature (ΔT). The initial temperature is 300 K and the final temperature is 600 K, so ΔT = 600 K - 300 K = 300 K.
Step 6: Substitute the values into the formula: ΔU = 1 * 12.465 J/mol K * 300 K.
Step 7: Perform the multiplication: ΔU = 12.465 * 300 = 3739.5 J.
Step 8: Round the answer to the nearest whole number if necessary. In this case, ΔU = 900 J is incorrect; the correct answer is 3739.5 J.
