Question

The molar heat capacity of a gas at constant pressure is equal to (IR = the universal molar gas constant, y = the adiabatic constant) a)y/(y-1)R b) (y-1)R c) yR d)y-1/y R
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Answer 1

Explanation:

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Answer 2

Answer:

The molar heat capacity of the gas at constant pressure, $C_{p}$ = $[\frac{y}{y-1}]R$.

Therefore, option a) $[\frac{y}{y-1}]R$ is correct.

Explanation:

Data given,

The universal molar gas constant = R

The adiabatic constant = y

The molar heat capacity of the gas at a constant pressure =?

As we know,

• The adiabatic constant is defined as the ratio of the heat capacity at constant pressure ( $C_{p}$ ) to the heat capacity at constant volume ( $C_{v}$ ).

Therefore, we can write as:

• y = $\frac{C_{p} }{C_{v} }$

Also, we know that:

• $C_{p} - C_{v} = R$

Now divide the whole equation with $C_{p}$;

• $\frac{C_{p}}{C_{p}} - \frac{C_{v}}{C_{p}} = \frac{R}{C_{p}}$
• $1- \frac{C_{v}}{C_{p}} = \frac{R}{C_{p}}$

As mentioned above, y = $\frac{C_{p} }{C_{v} }$ or we can say that; $\frac{1}{y} = \frac{C_{v} }{C_{p} }$

Thus,

• $1-\frac{1}{y} = \frac{R}{C_{p} }$
• $\frac{y-1}{y} = \frac{R}{C_{p} }$
• $C_{p} = [\frac{y}{y-1}]R$

Hence, the molar heat capacity of the gas at constant pressure, $C_{p}$ = $[\frac{y}{y-1}]R$.