To raise the temperature of a certain mass of gas by 50 ° C at a 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

Question

To raise the temperature of a certain mass of gas by 50 ° C at a 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)?

TestHub · Accepted Answer

At constant pressure : ∆ Q = nC P ∆ T ⇒ 160 = nC P . 50 .....(1) At constant volume ∆ Q = nC v ∆ T ⇒ 240 = nC v . 100 ......(2) Equation (1) divided by (2) 160 240 = C P C V · 50 100 C P C V = 4 3 = 1 + 2 f f = 6

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