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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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Verified Answer
70 calories of heat are required to raise the temperature of 2 moles o...
Cp= q/n*delta t
= 70/2*5=7
We know that for diatomic gas
Cp/Cv=7/5
So Cv=5
Cv=q/n*delta t
5=q/2*5
q=50 calories
Most Upvoted Answer
70 calories of heat are required to raise the temperature of 2 moles o...
Understanding Heat Capacity
To find the heat required to raise the temperature of an ideal gas at constant volume, we first need to understand the relationship between heat, temperature change, and heat capacities.
Given Data
- Heat at constant pressure (Qp) = 70 calories
- Temperature change (ΔT) = 35°C - 30°C = 5°C
- Number of moles (n) = 2 moles
- Gas constant (R) = 1.99 cal/K-mole
Heat at Constant Pressure
Using the formula for heat at constant pressure:
Qp = n * Cp * ΔT
Where Cp is the molar heat capacity at constant pressure.
Now, substituting the given values:
70 = 2 * Cp * 5
From this, we can calculate Cp:
Cp = 70 / (2 * 5) = 7 cal/K-mole
Heat at Constant Volume
For constant volume, we use the relationship between heat capacities:
Cp - Cv = R
We can find Cv (molar heat capacity at constant volume):
Cv = Cp - R
Cv = 7 - 1.99 = 5.01 cal/K-mole (approximately 5 cal/K-mole)
Now, we can calculate the heat required at constant volume (Qv):
Qv = n * Cv * ΔT
Qv = 2 * 5 * 5 = 50 calories
Conclusion
The heat required to raise the temperature of the gas at constant volume through the same range is nearly 50 calories. Therefore, the correct answer is option 'B'.
To find the heat required to raise the temperature of an ideal gas at constant volume, we first need to understand the relationship between heat, temperature change, and heat capacities.
Given Data
- Heat at constant pressure (Qp) = 70 calories
- Temperature change (ΔT) = 35°C - 30°C = 5°C
- Number of moles (n) = 2 moles
- Gas constant (R) = 1.99 cal/K-mole
Heat at Constant Pressure
Using the formula for heat at constant pressure:
Qp = n * Cp * ΔT
Where Cp is the molar heat capacity at constant pressure.
Now, substituting the given values:
70 = 2 * Cp * 5
From this, we can calculate Cp:
Cp = 70 / (2 * 5) = 7 cal/K-mole
Heat at Constant Volume
For constant volume, we use the relationship between heat capacities:
Cp - Cv = R
We can find Cv (molar heat capacity at constant volume):
Cv = Cp - R
Cv = 7 - 1.99 = 5.01 cal/K-mole (approximately 5 cal/K-mole)
Now, we can calculate the heat required at constant volume (Qv):
Qv = n * Cv * ΔT
Qv = 2 * 5 * 5 = 50 calories
Conclusion
The heat required to raise the temperature of the gas at constant volume through the same range is nearly 50 calories. Therefore, the correct answer is 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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