(C) Given: $C_p = 7.2 \, cal/mol \cdot K$,$R = 8.3 \, J/mol \cdot K$. Since $1 \, cal \approx 4.18 \, J$,we convert $R$ to $cal$: $R = 8.3 / 4.18 \app

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(C) Given: $C_p = 7.2 \, cal/mol \cdot K$,$R = 8.3 \, J/mol \cdot K$. Since $1 \, cal \approx 4.18 \, J$,we convert $R$ to $cal$: $R = 8.3 / 4.18 \approx 2 \, cal/mol \cdot K$.Molar heat capacity at constant volume is given by $C_v = C_p - R$.$C_v = 7.2 - 2 = 5.2 \, cal/mol \cdot K \approx 5 \, cal/mol \cdot K$.Number of moles $n = 5 \, mol$.Change in temperature $\Delta T = 20^\circ C - 10^\circ C = 10 \, K$.The heat required at constant volume is $\Delta Q = n C_v \Delta T$.$\Delta Q = 5 \times 5 \times 10 = 250 \, cal$.

Class 11 Physics Kinetic Theory of Gases Molar Specific Heat of gas and relation between them (Mayer's formula)

Medium

Molar specific heat of oxygen at constant pressure $C_p = 7.2 \, cal/mol \cdot ^\circ C$ and $R = 8.3 \, J/mol \cdot K$. At constant volume,$5 \, mol$ of oxygen is heated from $10^\circ C$ to $20^\circ C$. The quantity of heat required is approximately ........ $cal$.

A
$25$
B
$50$
C
$250$
D
$500$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Kinetic Theory of Gases

Subtopic

Molar Specific Heat of gas and relation between them (Mayer's formula)

Column-$I$ represents the type of gas and Column-$II$ represents the ${C_P}$ value for that type of gas. Match them correctly:
Column-$I$ Column-$II$
$(a)$ Monoatomic gas $(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration $(ii)$ ${C_P} = \frac{5}{2}R$
$(iii)$ ${C_P} = \frac{7}{2}R$
$(iv)$ ${C_P} = \frac{9}{2}R$

Easy

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$A$ cylinder with fixed capacity of $67.2 \, L$ contains helium gas at $STP$. The amount of heat needed to raise the temperature of the gas by $20 \, ^oC$ is ..... $J$ [Given that $R = 8.31 \, J \, mol^{-1} \, K^{-1}$]

MediumJEE MAIN 2019

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$310 \ J$ of heat is required to raise the temperature of $2 \ moles$ of an ideal gas at constant pressure from $25^{\circ} C$ to $35^{\circ} C$. The amount of heat required to raise the temperature of the gas through the same range at constant volume is (in $J$)

MediumKCET 2007

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According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

EasyMHT CET 2024

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When a monoatomic gas is heated at constant pressure,what fraction of the heat energy supplied is used to increase the internal energy?

Medium

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Column-$I$	Column-$II$
$(a)$ Monoatomic gas	$(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration	$(ii)$ ${C_P} = \frac{5}{2}R$
	$(iii)$ ${C_P} = \frac{7}{2}R$
	$(iv)$ ${C_P} = \frac{9}{2}R$

Molar specific heat of oxygen at constant pressure $C_p = 7.2 \, cal/mol \cdot ^\circ C$ and $R = 8.3 \, J/mol \cdot K$. At constant volume,$5 \, mol$ of oxygen is heated from $10^\circ C$ to $20^\circ C$. The quantity of heat required is approximately ........ $cal$.

Similar Questions

$A$ cylinder with fixed capacity of $67.2 \, L$ contains helium gas at $STP$. The amount of heat needed to raise the temperature of the gas by $20 \, ^oC$ is ..... $J$ [Given that $R = 8.31 \, J \, mol^{-1} \, K^{-1}$]

$310 \ J$ of heat is required to raise the temperature of $2 \ moles$ of an ideal gas at constant pressure from $25^{\circ} C$ to $35^{\circ} C$. The amount of heat required to raise the temperature of the gas through the same range at constant volume is (in $J$)

According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

When a monoatomic gas is heated at constant pressure,what fraction of the heat energy supplied is used to increase the internal energy?

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