A certain amount of an ideal monoatomic gas needs 20J of heat energy to raise its temperature by 10degree Celsius at constant pressure. The heat needed for the same temperature rise at constant volume will be. A. 30j B. 12j C. 200j D. 215.3 j Plz give the solution?

Question

Answer

∆H is given at constant P

which is equals to nCpdT
Cp of monoatomic gas =5R/2

from here ,
n =4/5R

now at constant volume we have to calculate ∆U=nCvdT
Cv for monoatomic gas =3R/2

∆U=4/5R×3R/2×10
∆U=12J

Answer

20=nCp10 (1)
x=n×Cv10(2)
dividing 1and2
20/x=Cp/Cv

Cp/Cv for monoatomic=5/3

20/x=5/3

x=12

Answer

12 joule

Answer

The heat energy required to raise the temperature of a gas depends on whether the process is carried out at constant pressure or constant volume.

Given:
Heat energy required at constant pressure = 20 J
Change in temperature = 10 °C

To find:
Heat energy required at constant volume

Formula:
Heat energy (Q) = nCΔT

Where:
Q = Heat energy
n = Number of moles of gas
C = Molar heat capacity of the gas at constant pressure or volume
ΔT = Change in temperature

We know that for an ideal monoatomic gas, the molar heat capacity at constant volume (CV) is given by:
CV = (3/2)R

Where:
R = Universal gas constant = 8.314 J/(mol·K)

Let's calculate the number of moles of gas (n):
As the gas is an ideal monoatomic gas, we can use the ideal gas equation to calculate the number of moles:
PV = nRT

Where:
P = Pressure
V = Volume
T = Temperature
R = Universal gas constant

Since the pressure and volume are not given, we can assume they remain constant. Therefore, the number of moles of gas will remain constant.

Now, let's calculate the number of moles of gas using the ideal gas equation:
n = PV/RT

Since n remains constant, the number of moles of gas for both constant pressure and constant volume processes will be the same.

Therefore, the heat energy required at constant volume (Qv) can be calculated using the formula:
Qv = nCVΔT

Substituting the values:
CV = (3/2)R
ΔT = 10 °C

Qv = n(3/2)RΔT

Since n, R, and ΔT are constant, the heat energy required at constant volume will be:
Qv = (3/2)R * ΔT

Calculating the value:
Qv = (3/2) * 8.314 J/(mol·K) * 10 °C

Qv = 12.471 J

Therefore, the heat needed for the same temperature rise at constant volume is approximately 12 J (option B).

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