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Question

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In the figure above are four containers of gas, each initially with the same volume, temperature, and pressure. Containers A and B contain Helium, a monatomic ideal gas, and containers C and D contain Hydrogen, a diatomic ideal gas. Containers A and C have a constant volume, and containers B and D hold the gas at a constant pressure.

If the same amount of heat, Q, is added to each container, the temperatures will increase. Rank the containers in order from lowest to highest, according to their final temperatures after the heat Q is added.

Explanation / Answer

As no work is done,

Q = U (First law of thermodynamics)

Q = CvdT (Constant Volume process)

Q = CpdT (constant pressure process)

Since Q is same for all cases, the value of Cv and Cp decides dT(change in temperature)

Cv =3/2RT for monoatomic gas Cp=5/2RT for monoatomic gas

Cv =5/2RT for Diatomic gas   Cp=7/2RT for Diatomic gas

So lesser the Cv and Cp more will be dT

temperature change rank will be,

A > B = C > D

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