In an experiment 1.35 mole of helium is heated at constant pressure starting at 11𝑘. How much heat must be added to the gas to double its volume?

To determine how much heat needs to be added to 1.35 moles of helium gas to double its volume while keeping the pressure constant, we can use the principles of thermodynamics, specifically the ideal gas law and the concept of heat transfer. Let's break this down step by step.

Understanding the Ideal Gas Law

The ideal gas law is expressed as:

PV = nRT

Where:

• P = pressure (in atm or Pa)
• V = volume (in liters or cubic meters)
• n = number of moles of gas
• R = ideal gas constant (8.314 J/(mol·K))
• T = temperature (in Kelvin)

Initial Conditions

We start with 1.35 moles of helium at an initial temperature of 11 K. To double the volume, we need to understand how temperature and volume relate under constant pressure conditions.

Doubling the Volume

According to Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin, we can express this relationship as:

V1/T1 = V2/T2

Since we want to double the volume (V2 = 2V1), we can rewrite the equation:

V1/T1 = 2V1/T2

From this, we can derive:

T2 = 2T1

Substituting the initial temperature:

T2 = 2 × 11 K = 22 K

Calculating the Heat Added

To find the heat added (Q) to the gas, we can use the formula for heat transfer at constant pressure:

Q = nCpΔT

Where:

• n = number of moles (1.35 moles)
• Cp = molar heat capacity at constant pressure for helium (approximately 20.79 J/(mol·K))
• ΔT = change in temperature (T2 - T1)

Finding ΔT

Now, we can calculate the change in temperature:

ΔT = T2 - T1 = 22 K - 11 K = 11 K

Substituting Values into the Heat Equation

Now we can substitute the values into the heat equation:

Q = 1.35 moles × 20.79 J/(mol·K) × 11 K

Calculating this gives:

Q = 1.35 × 20.79 × 11 ≈ 314.57 J

Final Result

Therefore, the amount of heat that must be added to the helium gas to double its volume at constant pressure is approximately 314.57 Joules.

To determine how much heat must be added to 1.35 moles of helium gas to double its volume at constant pressure, we can use the ideal gas law and the concept of heat transfer in thermodynamics. Let's break this down step by step.

Understanding the Ideal Gas Law

The ideal gas law is expressed as:

PV = nRT

Where:

• P = pressure
• V = volume
• n = number of moles
• R = ideal gas constant (approximately 8.314 J/(mol·K))
• T = temperature in Kelvin

Initial Conditions

We start with 1.35 moles of helium at an initial temperature of 11 K. To double the volume, we need to find the final temperature when the volume is doubled while keeping the pressure constant.

Calculating the Final Temperature

Since we are doubling the volume (V_final = 2 * V_initial) and keeping pressure constant, we can rearrange the ideal gas law to find the relationship between temperature and volume:

V_initial / T_initial = V_final / T_final

Substituting the known values:

V_initial / T_initial = 2 * V_initial / T_final

By simplifying, we find:

T_final = 2 * T_initial

Now, substituting the initial temperature:

T_final = 2 * 11 K = 22 K

Calculating the Heat Added

To find the heat added (Q) at constant pressure, we use the formula:

Q = n * C_p * ΔT

Where:

• n = number of moles (1.35 moles)
• C_p = molar heat capacity at constant pressure for helium (approximately 20.79 J/(mol·K))
• ΔT = change in temperature (T_final - T_initial)

Calculating ΔT:

ΔT = T_final - T_initial = 22 K - 11 K = 11 K

Now, substituting the values into the heat equation:

Q = 1.35 moles * 20.79 J/(mol·K) * 11 K

Q = 1.35 * 20.79 * 11

Q ≈ 320.5 J

Final Result

Therefore, the amount of heat that must be added to the gas to double its volume at constant pressure is approximately 320.5 Joules.