Multiple choices question on specific heats of gases

In summary: Is this summary correct?In summary, two cylinders A and B containing equal amounts of an ideal diatomic gas at 300 K are given the same amount of heat. While the piston in A is free to move, the piston in B is fixed. The rise in temperature of the gas in A is 30 K, and using the ratio of specific heats for a diatomic gas, the rise in temperature of the gas in B is calculated to be 42 K. This is determined by the molar heat capacities of the gases at constant pressure and volume, where Q_A=nC_pΔT_A and Q_B=nC_vΔT_B, with Q_A=Q_B. Therefore, the answer to the given question
  • #1
WMDhamnekar
MHB
376
28
Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is
(A) 30 K
(B) 18 K
(C) 50 K
(D) 42 K

My answer is 42 K. Is this answer correct?
 
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  • #2
Okay, what do YOU understand about this problem? You titled it "specific heat" so you must know that specific heat has something to do with this. How is specific heat of a gas related to its temperature?
 
  • #3
Country Boy said:
Okay, what do YOU understand about this problem? You titled it "specific heat" so you must know that specific heat has something to do with this. How is specific heat of a gas related to its temperature?
The piston in the cylinder A is free to move. Hence pressure of the gas is constant and the heat is given to it at constant pressure. that means $ Q_A=nC_p \Delta T_A$ where,
Q is the heat supplied or needed to bring about a change in temperature ($\Delta T$) in 1 mole of a substance ;
n is the amount of gas in moles;
$C_p$ is the molar heat capacity of a body of given substance at constant pressure.

The piston of the cylinder B is fixed. Hence the volume of the gas is constant and the heat is given at constant volume i.e., $ Q_B= nC_v \Delta T_B$ where $C_v$ is the molar heat capacity of a body of substance at constant volume.
The ratio of specific heats for a diatomic gas is $\frac{C_p}{C_v}=\frac75=1.4$. The heat given to the two gases are equal, $Q_A =Q_B$
So,
$\Delta T_B = \frac{C_p}{C_v}\Delta T_A= 42 K$
 
  • #4
Looks good to me.
 

Related to Multiple choices question on specific heats of gases

1. What is specific heat?

Specific heat is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius.

2. How is specific heat measured?

Specific heat is measured by conducting experiments in which the substance is heated and its temperature change is recorded. The ratio of the heat energy input to the temperature change is the specific heat.

3. What is the specific heat of gases?

The specific heat of gases varies depending on the type of gas and its temperature. At constant pressure, the specific heat of gases is approximately 1.0 J/g°C. However, at constant volume, the specific heat of gases is approximately 0.7 J/g°C.

4. How does specific heat affect the behavior of gases?

The specific heat of gases plays a significant role in their behavior, particularly in terms of temperature changes. Gases with higher specific heat require more heat energy to increase their temperature, and therefore have a slower rate of temperature change compared to gases with lower specific heat.

5. How does specific heat relate to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. Specific heat is a measure of the energy required to change the temperature of a substance, and therefore, it is related to the first law of thermodynamics as it involves the transfer and conversion of energy.

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