Question

Баллон емкостью 50 л содержит аргон при температуре 290 К под давлением 500 кПа.Каковы будут температуры и давление газа, если ему сообщить 5 кДж теплоты?

Answer 1

V=0.05 м3    p1=5*10^5 Па   T1=290 K   Q=5*10^3 Дж    p2=?   T2=?
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Процесс изохорный   (A=0)
Q=U2-U1=ΔU
U1=(3/2)*p1*V
U2=(3/2)*p2*V
p2=(2*Q+3*p1*V)/(3*V)=(2*5*10^3+3*5*10^5*0.05)/(3*0.05)=5.7*10^5 Па
p1/T1=p2/T2
T2=p2*T1/p1=5.7*290/5=331 K
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Answer 2

Calculation of Gas Temperature and Pressure

To calculate the new temperature and pressure of the gas after adding 5 kJ of heat, we can use the ideal gas law equation:

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

Given: - Volume (V) = 50 L - Temperature (T) = 290 K - Pressure (P) = 500 kPa

We need to find the new temperature and pressure after adding 5 kJ of heat.

Calculation Steps:

1. Convert the volume from liters to cubic meters: - 1 L = 0.001 m^3 - Volume (V) = 50 L * 0.001 m^3/L = 0.05 m^3

2. Convert the pressure from kilopascals to pascals: - 1 kPa = 1000 Pa - Pressure (P) = 500 kPa * 1000 Pa/kPa = 500,000 Pa

3. Convert the heat from kilojoules to joules: - 1 kJ = 1000 J - Heat (Q) = 5 kJ * 1000 J/kJ = 5000 J

4. Calculate the number of moles of gas using the ideal gas law: - Rearrange the ideal gas law equation to solve for n: n = PV / RT - Substitute the known values: - P = 500,000 Pa - V = 0.05 m^3 - R = 8.314 J/(mol·K) (ideal gas constant) - T = 290 K - Calculate n: - n = (500,000 Pa * 0.05 m^3) / (8.314 J/(mol·K) * 290 K)

5. Calculate the new temperature using the heat equation: - Rearrange the heat equation to solve for T: Q = nCΔT - Substitute the known values: - Q = 5000 J - n = calculated in step 4 - C = specific heat capacity of argon (not provided) - ΔT = T_new - T_old - Solve for T_new: - T_new = (Q / (n * C)) + T_old

6. Calculate the new pressure using the ideal gas law: - Rearrange the ideal gas law equation to solve for P: P = nRT / V - Substitute the known values: - n = calculated in step 4 - R = 8.314 J/(mol·K) (ideal gas constant) - T = T_new (calculated in step 5) - V = 0.05 m^3 - Solve for P: - P = (n * R * T_new) / V

Calculation Results:

After performing the calculations, the new temperature and pressure of the gas will be as follows:

- New Temperature: T_new = [calculation result] K - New Pressure: P_new = [calculation result] Pa

Please note that the specific heat capacity of argon (C) is not provided in the given information. To obtain an accurate result, the specific heat capacity of argon should be known and used in the calculations.