Respuesta :
Answer : The temperature is, 500.78 K
Explanation :
According to the question, this is the case of isothermal reversible expansion of gas.
As per first law of thermodynamic,
[tex]q=\Delta U+w[/tex]
where,
[tex]\Delta U[/tex] = internal energy
q = heat
w = work done
As we know that, the term internal energy is the depend on the temperature and the process is isothermal that means at constant temperature.
So, at constant temperature the internal energy is equal to zero.
[tex]\Delta U=0[/tex]
[tex]q=w[/tex]
The expression used for work done will be,
[tex]w=nRT\ln (\frac{V_2}{V_1})[/tex]
where,
w = work done on the system = [tex]5.09\times 10^3J[/tex]
n = number of moles of gas = 3 moles
R = gas constant = 8.314 J/mole K
T = temperature of gas = ?
[tex]V_1[/tex] = initial volume of gas = [tex]0.163m^3[/tex]
[tex]V_2[/tex] = final volume of gas = [tex]0.245m^3[/tex]
Now put all the given values in the above formula, we get :
[tex]5.09\times 10^3J=-3mole\times 8.314J/moleK\times T\times \ln (\frac{0.245m^3}{0.163m^3})[/tex]
[tex]T=500.78K[/tex]
Thus, the temperature is, 500.78 K
The temperature is 500.78 K.
First law of Thermodynamics:
It states that the change in the internal energy of a system is the sum of the heat transferred and the work done. It is given by:
[tex]\triangle U= Q-W[/tex]
where,
Δ U = internal energy
q = heat
w = work done
Internal energy is the dependent on the temperature and the process that is given is isothermal i.e. at constant temperature.
So, at constant temperature the internal energy is equal to zero.
Work done can be given by,
[tex]w=nRTln(\frac{V_2}{V_1})[/tex]
where,
w = work done on the system = 50.9*10³ J
n = number of moles of gas = 3 moles
R = gas constant = 8.314 J/mole K
T = temperature of gas = ?
V₁ = initial volume of gas = 0.163m³
V₂ = final volume of gas = 0.254m³
On substituting the values in the above formula we will get:
[tex]w=nRTln(\frac{V_2}{V_1})\\\\5.09*10^3J=3*8.314*T*ln(\frac{0.245m^3}{0.163m^3})\\\\T=500.78K[/tex]
Thus, the temperature is 500.78 K.
Find more information about First law of thermodynamics here:
brainly.com/question/1613201
