Question

n mole of an ideal gas with constant volume heat capacity CV​ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is?

Answer 1

here, we use the expression of work done in an isobaric process, where the pressure is constant. Comparing this relation with the change in heat expression that we get from the first law of thermodynamics will give us the required expression.

Formula used:
\eqalign{ & w = nR\Delta T \cr & \Delta H = ({C_{v}} + nR)\Delta T \cr}

Complete step-by-step answer:
An isobaric process occurs at constant pressure. As the pressure is constant, the force exerted is constant and therefore the work done is given by PdV.
We also know about an isobaric expansion i.e., if a gas is to expand at a constant pressure, heat should be transferred into the system at a certain rate.
The relation of temperature and work done in an isobaric process is given by:
\eqalign{ & w = nR\Delta T \cr & \Delta H = ({C_{v}} + nR)\Delta T \cr & \therefore \dfrac{w}{{\Delta H}} = \left( {\dfrac{{nR}}{{{C_v} + nR}}} \right) \cr}
Here, w is work done, n is no. of moles, R is gas constant, T is the temperature change. Also, H is the heat change.
Therefore, we get the required relation between work done and heat change in an isobaric process.

Additional Information: There are 4 laws of thermodynamics, the first law of thermodynamics states that internal energy change of a system equals net heat transfer minus net work done by the system.
There are four processes of heat transfer i.e., isobaric process, isothermal process, isochoric and adiabatic process.
We know that, in an isochoric process the volume is held constant, meaning that the work done by the system will be zero. This process is also known as an isometric process or an iso- volumetric process.
An isothermal process is a change of a system, in which the temperature remains constant- ΔT = 0. This happens when a system is in contact with an outside thermal reservoir or a heat bath, and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. We know that an adiabatic process is where a system exchanges no heat with its surroundings.

Note: The four laws of thermodynamics are first law, second law, third law and the 0th law. The heat in adiabatic processes is zero. Also, the subtraction of specific heat capacity at constant pressure and specific heat capacity at constant volume gives the gas constant.