Question

Одноатомний ідеальний газ об’ємом 1,0·10(у –3 степені)м3 перебуває під легкорухомим поршнем циліндра за тиску 1,6·10(у5 степені) Па. Яку кількість теплоти потрібно передати газу, щоб у ході йогоізобарного розширення об’єм газу збільшився у 2 рази?

Answer 1

Если я все правильно поняла, то возможнорешение будет следующее:

Q=ΔU+A'

A'=pΔV

ΔU=3/2m/MRΔT=(используя Уравнение pΔV=m/MRΔT-- делаем замену)=3/2pΔV

Q=3/2pΔV+pΔV=5/2pΔV=5/2·1.6·10⁵·1·10⁻³=4·10²=400Дж

Answer 2

To find the amount of heat required to double the volume of the ideal gas during its isobaric expansion, we can use the formula for the work done during an isobaric process and the first law of thermodynamics.

Formula for work done during an isobaric process:

The work done during an isobaric process is given by the formula:

W = P * ΔV

Where: - W is the work done - P is the pressure - ΔV is the change in volume

First law of thermodynamics:

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

ΔU = Q - W

Where: - ΔU is the change in internal energy - Q is the heat added to the system - W is the work done by the system

Solution:

Given: - Volume of the gas (V) = 1.0 * 10^(-3) m^3 - Pressure (P) = 1.6 * 10^5 Pa - Change in volume (ΔV) = 2 * V = 2 * 1.0 * 10^(-3) m^3

To find the amount of heat required to double the volume of the gas, we need to calculate the work done during the isobaric expansion and then use the first law of thermodynamics to find the heat added.

1. Calculate the work done: - Using the formula for work done during an isobaric process, we have: W = P * ΔV - Substituting the given values, we get: W = (1.6 * 10^5 Pa) * (2 * 1.0 * 10^(-3) m^3) - Simplifying the expression, we find: W = 3.2 * 10^2 J

2. Calculate the heat added: - Using the first law of thermodynamics, we have: ΔU = Q - W - Since the gas is an ideal gas, the change in internal energy (ΔU) is given by: ΔU = n * Cv * ΔT - Where n is the number of moles of the gas, Cv is the molar specific heat at constant volume, and ΔT is the change in temperature. - Since the process is isobaric, the change in temperature (ΔT) is given by: ΔT = P * ΔV / (n * R) - Where R is the ideal gas constant. - Substituting the values, we have: Q - W = n * Cv * (P * ΔV / (n * R)) - Simplifying the expression, we find: Q = W + n * Cv * (P * ΔV / (n * R)) - Since we are given the volume and pressure, we can calculate the number of moles of the gas using the ideal gas equation: n = P * V / (R * T) - Where T is the temperature in Kelvin. - Substituting the values, we have: Q = W + (P * V / (R * T)) * Cv * (P * ΔV / (P * V / (R * T))) - Simplifying the expression, we find: Q = W + Cv * P * ΔV / T

3. Calculate the heat added: - Substituting the given values, we have: Q = 3.2 * 10^2 J + Cv * (1.6 * 10^5 Pa) * (2 * 1.0 * 10^(-3) m^3) / T - Since we don't have the specific heat capacity at constant volume (Cv) and the temperature (T), we cannot calculate the exact value of Q without additional information.

Please note that the calculation above assumes that the gas behaves ideally and that the specific heat capacity at constant volume (Cv) is constant over the given temperature range.