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To raise the temperature of a certain mass of gas by 50°C at constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Asked in JEE Main 3rd Sept 2nd Shift 2020 · Cv, Cp and Mayer's relation

• (1) 5
• (2) 6
• (3) 3
• (4) 7

Step-by-step solution

Why the other options are wrong

• (1) Assumes a rigid diatomic instead of reading γ off the two measurements.
• (3) Assumes a monoatomic gas, which would give γ=5/3, not 4/3.
• (4) Comes from inverting the ratio of the two heats, which gives a γ below 1.

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