A monoatomic ideal gas undergoes thermodynamic process according to relation pt²=constant. If molar heat capacity of gas at cv then it's molar heat capacity of given process is

To find the molar heat capacity of the given process, we can use the relation pt² = constant.

First, let's recall the definition of molar heat capacity. Molar heat capacity (Cv) is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant volume.

In this case, we are given the relation pt² = constant. This implies that the product of pressure (p) and temperature squared (t²) remains constant throughout the process.

To find the molar heat capacity of the given process, we need to differentiate the relation pt² = constant with respect to temperature (t) at constant volume (v).

Differentiating both sides of the equation, we get:

2pt dp + 2t² dp/dt = 0

Since the process is at constant volume, dp/dt = 0. Therefore, the equation simplifies to:

2pt dp = 0

Now, let's recall the definition of molar heat capacity at constant volume (Cv):

Cv = (dQ/dt)v

Where dQ is the heat added to the system and dt is the change in temperature.

Since the process is at constant volume, dQ = Cv dt.

Substituting this into the equation 2pt dp = 0, we get:

2pt Cv dt = 0

Dividing both sides by dt, we get:

2pt Cv = 0

Simplifying further, we find:

Cv = 0

Therefore, the molar heat capacity of the given process is zero.