Question

An ideal gas uses 25% of heat supplied to do work.
Assume Y =
Cp/Cv
The molar specific heat is
(1) 2R
(2) 4R
4R/3(r-1)
(4) 2R​

Answer 1

Answer:

2R answer....................

Answer 2

Answer:

2) 4R

The molar specific heat is 4R.

Explanation:

Molar specific heat capacity is the amount of heat energy required to raise the temperature of 1 mole of a substance by 1 Kelvin.

$\Delta Q= nC \Delta T$

where, $n$ is no. of moles

$C$ is the specific heat capacity.

$T$ is the temperature

$\implies C = \frac{\Delta Q}{\Delta T}$   [for n= 1 mole]

Let, the total heat supplied be $\Delta Q$

Heat supplied to do work = 25% of heat supplied $= \frac{\Delta Q}{4}=\Delta W = PdV=$ Work done by gas

Using Ideal gas equation,

$PV=nRT$

Differentiating,

$\implies PdV=nRdT$

$\implies \frac{\Delta Q}{4} = nR\Delta T$

$\implies \frac{\Delta Q}{\Delta T}=4R$   [for n=1 mole]

$\implies C = 4R$

The molar specific heat is 4R.

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