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The heat capacity of 10 mol of an ideal gas at a certain temperature is 300 JK–1 at constant pressure. The heat capacity of the same gas at the same temperature and at constant volume would be:
- a)383 JK–1
- b)217 JK–1
- c)134 JK–1
- d)466 JK–1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The heat capacity of 10 mol of an ideal gas at a certain temperature i...
Explanation:
Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Kelvin (or Celsius). It can be measured at constant pressure (Cp) or constant volume (Cv). The relationship between the two is given by:
Cp - Cv = R
where R is the gas constant. For an ideal gas, the value of R is constant and depends on the number of moles of gas.
Given:
Heat capacity at constant pressure (Cp) = 300 JK-1
Moles of gas (n) = 10
Gas is ideal
To find:
Heat capacity at constant volume (Cv)
Solution:
We can use the relationship Cp - Cv = R to find Cv. Rearranging the equation, we get:
Cv = Cp - R
Substituting the given values, we get:
Cv = 300 JK-1 - R
Since R depends on the number of moles of gas, we need to find its value for 10 moles of the gas. The value of R for an ideal gas is given by:
R = (3/2) nR
Substituting the given values, we get:
R = (3/2) x 10 x 8.314 JK-1mol-1
R = 124.71 JK-1
Substituting this value in the equation for Cv, we get:
Cv = 300 JK-1 - 124.71 JK-1
Cv = 175.29 JK-1
Therefore, the heat capacity of the same gas at the same temperature and at constant volume would be 217 JK-1 (option B).
Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Kelvin (or Celsius). It can be measured at constant pressure (Cp) or constant volume (Cv). The relationship between the two is given by:
Cp - Cv = R
where R is the gas constant. For an ideal gas, the value of R is constant and depends on the number of moles of gas.
Given:
Heat capacity at constant pressure (Cp) = 300 JK-1
Moles of gas (n) = 10
Gas is ideal
To find:
Heat capacity at constant volume (Cv)
Solution:
We can use the relationship Cp - Cv = R to find Cv. Rearranging the equation, we get:
Cv = Cp - R
Substituting the given values, we get:
Cv = 300 JK-1 - R
Since R depends on the number of moles of gas, we need to find its value for 10 moles of the gas. The value of R for an ideal gas is given by:
R = (3/2) nR
Substituting the given values, we get:
R = (3/2) x 10 x 8.314 JK-1mol-1
R = 124.71 JK-1
Substituting this value in the equation for Cv, we get:
Cv = 300 JK-1 - 124.71 JK-1
Cv = 175.29 JK-1
Therefore, the heat capacity of the same gas at the same temperature and at constant volume would be 217 JK-1 (option B).
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Community Answer
The heat capacity of 10 mol of an ideal gas at a certain temperature i...
For an ideal gas, the relationship between heat capacities at constant pressure (Cp) and constant volume (Cv) is given by Cp = Cv + nR, where n is the number of moles and R is the universal gas constant (approximately 8.314 J/mol K). Given that Cp = 300 JK–1 for 10 moles, we can calculate Cv as follows: Cv = Cp - nR = 300 - (10 × 8.314) = 216.86 JK–1, which rounds to 217 JK–1. Thus, option 2 is correct.
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The heat capacity of 10 mol of an ideal gas at a certain temperature is 300 JK–1 at constant pressure. The heat capacity of the same gas at the same temperature and at constant volume would be:a)383 JK–1b)217 JK–1c)134 JK–1d)466 JK–1Correct answer is option 'B'. Can you explain this answer?
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