A gram molecule of a gas at 127°C expands isothermally until its volume is doubled. Find the amount of work done and heat absorbed.
The formula you will use for isothermic expansion is:
Work(W) = 2.303 RT log(V2/V1)
Let R = 8.3 J / mole-K (universal gas constant and V2/v1 = 2/1 = 2.
Converting temperature to Kelvins:
T = 127°C = 400K
Work(W) = (2.3)(8.3)(400)log(2)
W = 2.3 x 10^3 J
To find the heat absorbed:
2.3 x 10^3 J/4.2 = 548 cal.
One gram molecule of an ideal gas at 127°C expands isothermally until volume is doubled ,find the amount of work done given log=0.3010 R=8.31×10erg mol-¹°c
To find the amount of work done and heat absorbed during the isothermal expansion of a gas, we can use the following formulas:
1. Work done (W) = nRT * ln(Vf/Vi)
2. Heat absorbed (Q) = nRT * ln(Vf/Vi)
Where:
- n = moles of gas
- R = ideal gas constant
- T = temperature in Kelvin
- Vi = initial volume
- Vf = final volume
Given:
- n = 1 gram molecule, which is equal to 1 mole
- T = 127°C -> convert to Kelvin: T = 127 + 273.15 = 400.15 K
- Vi = initial volume
- Vf = 2 * Vi (since the volume is doubled)
Let's substitute these values into the formulas:
Work done (W) = (1 mole) * (R) * (400.15 K) * ln(2 * Vi / Vi)
Heat absorbed (Q) = (1 mole) * (R) * (400.15 K) * ln(2 * Vi / Vi)
Since the initial volume Vi cancels out in both formulas, we can simplify them further:
Work done (W) = (1 mole) * (R) * (400.15 K) * ln(2)
Heat absorbed (Q) = (1 mole) * (R) * (400.15 K) * ln(2)
The value of R is approximately 8.314 J/(mol·K). Now we can calculate the work done and heat absorbed during the expansion.
To find the amount of work done and heat absorbed during the isothermal expansion of a gas, we can follow these steps:
1. Determine the given information:
- Temperature: 127°C (which needs to be converted to Kelvin)
- Volume change: doubled (which means final volume = 2 * initial volume)
- Amount of gas: 1 gram molecule
2. Convert temperature from Celsius to Kelvin:
- To convert from Celsius (°C) to Kelvin (K), we add 273.15 to the Celsius temperature.
Conversion: 127°C + 273.15 = 400.15 K
3. Determine the ideal gas constant (R):
- The ideal gas constant (R) is a constant value that depends on the units of pressure, volume, temperature, and the amount of gas. For simplicity, we'll use the value of R = 0.0821 L·atm/(mol·K).
4. Calculate the initial volume (V1):
- Since the volume is doubled during the expansion, the final volume (V2) is 2 times the initial volume (V1).
- Given that V2 = 2 * V1, we need to solve for V1.
5. Calculate the work done (W):
- The formula for work done during an isothermal expansion of a gas is: W = -nRT ln(V2/V1), where n is the number of moles of gas, R is the ideal gas constant, T is the temperature in Kelvin, V2 is the final volume, and V1 is the initial volume.
- Since n = 1 gram molecule and we know R (0.0821 L·atm/(mol·K)), T (400.15 K), V2 (2 * V1), and V1 (calculated in step 4), we can substitute these values into the formula to find the work done.
6. Calculate the heat absorbed (Q):
- For an isothermal process, the change in internal energy (ΔU) is zero. Since ΔU = Q - W, we can conclude that Q (heat absorbed) is equal to -W (work done).
So, by calculating the work done (W), we can find the heat absorbed (Q) during the isothermal expansion of the gas.