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What is the variation of cp, cv and k in case of gases when the temperature increases?
- a)cp and cv decreases with temperature, and k increases
- b)cp and cv increase with temperature, and k decreases
- c)cp and cv increase with temperature, and k increases
- d)cp and cv decreases with temperature, and k decreases
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the variation of cp, cv and k in case of gases when the temper...
Explanation: cp is molar heat capacity at constant pressure. As temperature is increased, enthalpy increases, heat capacity increases.
Same is for cv, cp is molar heat capacity at constant volume.
However cp-cv=R and cp/cv = R
Hence, as cp, cv increases R decreases.
Same is for cv, cp is molar heat capacity at constant volume.
However cp-cv=R and cp/cv = R
Hence, as cp, cv increases R decreases.
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What is the variation of cp, cv and k in case of gases when the temper...
Variation of Cp, Cv and k with Temperature in Gases
Cp and Cv are the specific heats of gases at constant pressure and constant volume, respectively, while k represents the ratio of Cp to Cv. The behavior of these properties with temperature can be explained as follows:
Increase in Temperature
As the temperature of a gas increases, the molecules gain more kinetic energy and move faster, leading to an increase in internal energy. This results in the following changes:
- Cp and Cv increase with temperature: The increase in temperature leads to an increase in the number of available modes of motion for the gas molecules, increasing their internal energy. This causes Cp and Cv to increase, as more energy is required to raise the temperature of the gas.
- k decreases with temperature: The increase in internal energy also causes an increase in the degree of freedom of the gas molecules, making them more likely to move in all directions. This results in a decrease in the ratio of Cp to Cv, as the gas becomes more compressible.
Therefore, option B is correct, as it states that Cp and Cv increase with temperature, while k decreases. This is consistent with the behavior of gases at high temperatures.
Cp and Cv are the specific heats of gases at constant pressure and constant volume, respectively, while k represents the ratio of Cp to Cv. The behavior of these properties with temperature can be explained as follows:
Increase in Temperature
As the temperature of a gas increases, the molecules gain more kinetic energy and move faster, leading to an increase in internal energy. This results in the following changes:
- Cp and Cv increase with temperature: The increase in temperature leads to an increase in the number of available modes of motion for the gas molecules, increasing their internal energy. This causes Cp and Cv to increase, as more energy is required to raise the temperature of the gas.
- k decreases with temperature: The increase in internal energy also causes an increase in the degree of freedom of the gas molecules, making them more likely to move in all directions. This results in a decrease in the ratio of Cp to Cv, as the gas becomes more compressible.
Therefore, option B is correct, as it states that Cp and Cv increase with temperature, while k decreases. This is consistent with the behavior of gases at high temperatures.
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What is the variation of cp, cv and k in case of gases when the temperature increases?a)cp and cv decreases with temperature, and k increasesb)cp and cv increase with temperature, and k decreasesc)cp and cv increase with temperature, and k increasesd)cp and cv decreases with temperature, and k decreasesCorrect answer is option 'B'. Can you explain this answer?
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