Question

Consider a constant volume process involving heat addition to a closed system consisting of an ideal gas with no changes in kinetic or potential energy. Is the required heat transfer for raising the temperature from 295 to 305 K the same as the heat transfer required from 345 to 355 K?

Answer 1

Answer:

Yes and no

Explanation:

The thermodynamic equation for the heat transfer in a constant volume process is the following:

$Q=\Delta U=mC_V\Delta T$

where Q is the required heat, U is the internal energy, m the mass of the gas, C_V the heat capacity assuming consant volume and $\Delta T$ is the change in temperature.

If you assume the heat capacity doesn't change with temperature at which the gas is currently at then the heat transfer depends solely on the change in temperature. With this assumption the transfered heat would be the same in both cases.

In reality the heat capacity does change with respect to temperature. Depending on the type of gas. In reality there would be difference in heat transfered between 295/205 K and 245/255 . Only then you wouldn't use the $\Delta T$ expression since the integral would be different depending on the heat capacity in relation to temperature.