Question 1: Thermodynamics & KTG

Question

Two moles of ideal helium gas are in a rubber balloon at 30
o
C. The balloon is fully expandable
and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35
o
C. The amount of heat required in raising the temperature is
nearly (take R = 8.31 J/mol.K)

Accepted Answer

Here's a breakdown of how to solve this problem:
Understanding the Concepts
Ideal Gas:
An ideal gas is a theoretical gas that follows the ideal gas law perfectly. The ideal gas law is a relationship between pressure ($P$), volume ($V$), temperature ($T$), and the number of moles ($n$) of a gas:
$PV = nRT$, where $R$ is the ideal gas constant.
Heat Capacity:
Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius (or 1 Kelvin).  For an ideal gas, we can use the specific heat capacity at constant volume ($C_v$) or at constant pressure ($C_p$).
Constant Volume Process:
In a constant volume process, the volume of the gas remains constant. The heat required to raise the temperature is given by:
$Q = nC_v\Delta T$
Constant Pressure Process:
In a constant pressure process, the pressure of the gas remains constant. The heat required to raise the temperature is given by:
$Q = nC_p\Delta T$
Molar Heat Capacities of Helium:
Helium is a monatomic gas. For monatomic gases, we have:
$C_v = \frac{3}{2}R$
$C_p = \frac{5}{2}R$
Solving the Problem
Identify the Process:
Since the balloon is fully expandable, the pressure remains constant. This is a constant pressure process.
Calculate the Heat:
Use the formula for heat at constant pressure:
$Q = nC_p\Delta T$
Substitute the Values:
$n = 2 	ext{ moles}$
$C_p = \frac{5}{2}R = \frac{5}{2}(8.31 	ext{ J/mol.K})$
$\Delta T = 35^\circ C - 30^\circ C = 5 K$
Solve for Q:
$Q = (2 	ext{ moles}) 	imes \left(\frac{5}{2} 	imes 8.31 	ext{ J/mol.K}ight) 	imes (5 K) $
$Q = 207.75 	ext{ J}$
Answer:
The amount of heat required to raise the temperature of the helium gas is approximately
208 J
.  Therefore, the correct answer is
Option D
.

Answer

62 J

Answer

104 J

Answer

124 J

Answer

208 J

Thermodynamics & KTG

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