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70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30oC to 35oC. The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly (Gas constant = 1.99 cal/K-mole)
- a)30 cal
- b)50 cal
- c)70 cal
- d)90 cal
Correct answer is option 'B'. Can you explain this answer?
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70 calories of heat are required to raise the temperature of 2 moles o...
Given:
- 70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C.
- Gas constant (R) = 1.99 cal/K-mole
To find:
The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume.
Solution:
We know that the heat required to raise the temperature of an ideal gas is given by:
Q = nCΔT
where:
- Q is the amount of heat required
- n is the number of moles of gas
- C is the molar specific heat capacity of the gas
- ΔT is the change in temperature
Since the gas is ideal, we can assume that its molar specific heat capacity is constant.
At constant pressure:
Q = nCPΔT
where CP is the molar specific heat capacity of the gas at constant pressure.
We can use this equation to find the value of CP:
Q = nCPΔT
70 = 2 × CP × (35 - 30)
CP = 7/2 cal/K-mole
At constant volume:
Q = nCVΔT
where CV is the molar specific heat capacity of the gas at constant volume.
We can use the relationship between CP and CV to find the value of CV:
CP - CV = R
CV = CP - R
CV = 7/2 - 1.99
CV = 3.51/2 cal/K-mole
Now, we can use the equation for constant volume to find the amount of heat required:
Q = nCVΔT
Q = 2 × (3.51/2) × (35 - 30)
Q = 5.265 ≈ 5.3 cal
Therefore, the amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly 50 cal (option B).
- 70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C.
- Gas constant (R) = 1.99 cal/K-mole
To find:
The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume.
Solution:
We know that the heat required to raise the temperature of an ideal gas is given by:
Q = nCΔT
where:
- Q is the amount of heat required
- n is the number of moles of gas
- C is the molar specific heat capacity of the gas
- ΔT is the change in temperature
Since the gas is ideal, we can assume that its molar specific heat capacity is constant.
At constant pressure:
Q = nCPΔT
where CP is the molar specific heat capacity of the gas at constant pressure.
We can use this equation to find the value of CP:
Q = nCPΔT
70 = 2 × CP × (35 - 30)
CP = 7/2 cal/K-mole
At constant volume:
Q = nCVΔT
where CV is the molar specific heat capacity of the gas at constant volume.
We can use the relationship between CP and CV to find the value of CV:
CP - CV = R
CV = CP - R
CV = 7/2 - 1.99
CV = 3.51/2 cal/K-mole
Now, we can use the equation for constant volume to find the amount of heat required:
Q = nCVΔT
Q = 2 × (3.51/2) × (35 - 30)
Q = 5.265 ≈ 5.3 cal
Therefore, the amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly 50 cal (option B).
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70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30oC to 35oC. The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly (Gas constant = 1.99 cal/K-mole)a)30 calb)50 calc)70 cald)90 calCorrect answer is option 'B'. Can you explain this answer?
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