Question

Газ при температуре 100 С° и давлении 10^5 Па изотермически сжат до давления 1,5*10^5 Па. До какой температуры нужно изохорически охладить этот газ, чтобы давление понизилось до первоначального значения

Answer 1

Сначала изотермически ( при пост. тепм. ) сжали в полтора раза. pv=const, т. е. объём уменьшился в те же полтора раза. если было v, стало 0.667v
теперь если охлаждать при постоянном объеме ( изохора ), то p/T = const, только T надо считать в K.
было 373K, надо стало быть теперь темп. понизить в 1,5 раза, до 248.7K, или -24.3град. С

Answer 2

Gas Compression and Temperature Change

To calculate the final temperature after isothermally compressing the gas from a pressure of 10^5 Pa to 1.5*10^5 Pa, we can use the ideal gas law, which states that for an isothermal process (constant temperature), the pressure and volume of a gas are inversely proportional. The formula for the ideal gas law is:

P1 * V1 = P2 * V2

Where: - P1 = initial pressure - V1 = initial volume - P2 = final pressure - V2 = final volume

In this case, the initial pressure (P1) is 10^5 Pa, and the final pressure (P2) is 1.5*10^5 Pa. Since the process is isothermal, the initial and final temperatures are the same.

Using the ideal gas law, we can calculate the final volume (V2) in terms of the initial volume (V1):

V2 = (P1 * V1) / P2

Now, to find the temperature at which the gas needs to be isochorically cooled to return to the initial pressure, we can use the combined gas law, which states that for a constant amount of gas, the pressure, volume, and temperature are related by the equation:

P1 * V1 / T1 = P2 * V2 / T2

Where: - T1 = initial temperature - T2 = final temperature

Since the initial and final pressures are the same, the equation simplifies to:

V1 / T1 = V2 / T2

Rearranging for T2, we get:

T2 = T1 * (V2 / V1)

Now, we can substitute the value of V2 from the isothermal compression equation into the temperature equation to find the final temperature.

Let's calculate the final temperature using the given values.

Calculation

Using the given values: - P1 = 10^5 Pa - P2 = 1.5*10^5 Pa - T1 = 100°C (initial temperature)

We can calculate V2 using the isothermal compression equation: V2 = (P1 * V1) / P2

Then, we can use the calculated V2 to find the final temperature T2: T2 = T1 * (V2 / V1)

Result

The final temperature T2 at which the gas needs to be isochorically cooled to return to the initial pressure can be calculated using the above method.

Let's proceed with the calculations and find the final temperature T2.