How much energy (in 107 Joules) is absorbed by 10kg molecule of an ideal gas if it expands from its initial pressure of 8 atm to 4 atm at a constant temperature of 27ºC.Correct answer is '1.728'. Can you explain this answer?

Question

How much energy (in 107 Joules) is absorbed by 10kg molecule of an ideal gas if it expands from its initial pressure of 8 atm to 4 atm at a constant temperature of 27&ordm;C.Correct answer is '1.728'. Can you explain this answer?

Answer

To calculate the energy absorbed by the gas, we can use the equation:

ΔU = nCvΔT

Where:
ΔU is the change in internal energy of the gas
n is the number of moles of the gas
Cv is the molar specific heat capacity at constant volume of the gas
ΔT is the change in temperature of the gas

Given:
P1 (initial pressure) = 8 atm
P2 (final pressure) = 4 atm
T (constant temperature) = 27 °C = 27 + 273 = 300 K
Mass of the gas (m) = 10 kg
Molar mass of the gas (M) = ? (Not provided)

To calculate the molar mass (M) of the gas, we can use the formula:

M = m / n

Where:
m is the mass of the gas
n is the number of moles of the gas

To find the number of moles (n) of the gas, we can use the formula:

n = m / M

Let's calculate the molar mass (M) of the gas:

M = m / n
M = 10 kg / n

Now, we need to find the number of moles (n) of the gas. To do that, we need the molar mass of the gas. Since the molar mass is not provided, we cannot calculate the number of moles and, consequently, the energy absorbed by the gas.

Therefore, we cannot determine the energy (in 10^7 Joules) absorbed by the 10 kg molecule of the ideal gas without the molar mass of the gas.

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