Question

Ideal monoatomic gas is taken through a
process dQ = 2dU. The molar heat
capacity for the process is : (where da is
heat supplied and du change in internal
energy R is universal gas constant)
(A)
5 R​

Answer 1

The molar heat  capacity for the process is 3R.

Explanation:

dQ = 2 × dU

Now,

dU = n × Cv × dT → (equation 1)

On substituting equation (1) in given equation, we get,

dQ = 2 × (n × Cv × dT)

Now, the molar heat capacity is given as:

n × c × dT = 2 × (n × Cv × dT)

∴ c = 2 × Cv → (equation 2)

Now, for ideal monoatomic gas,

Cv = (3 × R)/2

On substituting above equation in equation (2), we get,

c = 2 × (3 × R)/2

∴ c = 3R