Question

Газ, що займає об'єм 5л і знаходиться під тиском 0,2 МПа при температурі 17°С, був нагрітий та розширився ізобарвно. Робота розширення газу при цьому виявилася рівно 196,2 Дж. На скільки нагріли газ?

Answer 1

Газ, занимающий объем 5л и находящийся под давлением 0,2 МПа при температуре 17°С, был нагрет и расширился изобарно. Работа расширения газа при этом оказалась ровно 196,2 Дж. На сколько нагрели газ?

Answer 2

Expansion of Gas and Calculation of Heat

When a gas is heated, it expands and its volume increases. In this case, we have a gas with an initial volume of 5 liters and a pressure of 0.2 MPa at a temperature of 17°C. The gas is heated and expands isobarically (at constant pressure). The work done by the gas during expansion is given as 196.2 J. We need to calculate the amount by which the gas was heated.

Calculation Steps

To calculate the change in temperature of the gas, we can use the formula for the work done by a gas during expansion:

Work done (W) = Pressure (P) * Change in Volume (ΔV)

Since the pressure remains constant during the expansion, we can rewrite the formula as:

W = P * ΔV

We know that the work done by the gas during expansion is 196.2 J. We also know that the initial volume of the gas is 5 liters. To find the change in volume (ΔV), we can rearrange the formula:

ΔV = W / P

Substituting the given values, we have:

ΔV = 196.2 J / 0.2 MPa

Conversion of Units

Before we can calculate the change in volume, we need to convert the units of pressure and work done to a consistent unit system. Let's convert the pressure from megapascals (MPa) to pascals (Pa) and the work done from joules (J) to pascals (Pa).

1 MPa = 1,000,000 Pa 1 J = 1 Pa

Converting the pressure and work done:

Pressure (P) = 0.2 MPa = 0.2 * 1,000,000 Pa = 200,000 Pa Work done (W) = 196.2 J = 196.2 Pa

Calculation of Change in Volume

Now, we can calculate the change in volume (ΔV) using the converted values:

ΔV = 196.2 Pa / 200,000 Pa

Simplifying the expression:

ΔV = 0.000981 m^3

Calculation of Change in Temperature

To calculate the change in temperature (ΔT) of the gas, we can use the ideal gas law:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of gas - R is the ideal gas constant - T is the temperature of the gas

Since the pressure and volume of the gas remain constant during the expansion, we can rewrite the formula as:

T = (W / nR) + T_initial

We know the work done by the gas during expansion (W) and the initial temperature of the gas (T_initial). However, we don't have information about the number of moles of gas (n) or the ideal gas constant (R). Without this information, we cannot calculate the change in temperature of the gas.

Therefore, based on the given information, we cannot determine the exact change in temperature of the gas.