Question

An ideal monoatomic gas at temperature `27^@C` and pressure `10^6N//m^2` occupies 10L volume. 10,000 cal of heat is added to the system without changing the volume. Calculate the change in temperature of the gas. Given : `R=8.31 J//mol-K` and `J=4.18J//cal.`

Answer 1

Correct Answer - C
For n moles of gas, we have `pV=nRT`
Here, `p=10^6N//m^2`, `V=10` `L=10^-2m^3` and `T=27^@C=300K`
`:.` `n=(pV)/(RT)=(10^6xx10^-2)/(8.31xx300)=4.0`
For monatomic gas, `C_V=3/2R`
Thus, `C_V=3/2xx8.31J//mol-K`
`=3/2xx(8.31)/(4.18)=3cal//mol-K`
Let `DeltaT` be the rise in temperature when `n` moles of the gas is given Q cal of heat at constant volume. Then,
`Q=nC_VDeltaT` or `DeltaT=(Q)/(nC_V)`
`(10000cal)/(4.0mol exx3cal//mol-K)`
`=883K`