Answer to Question #209807 in Molecular Physics | Thermodynamics for Fhulu

Question

1.) A cooler bag at a beach party contains 12 cans of fizzy drinks at 5° C. Each can has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg.K). Someone adds a 6 5 kg watermelon at 27° C to the bag. The specific heat capacity of watermelon is nearly the same as that of water, i.e. 4.184 J/(kg.K). Ignore the little heat lost to the cooler bag and the environment. Calculate the final temperature T of the fizzy drinks and watermelon.

2.) Three moles of an ideal gas are compressed from 5.5×10^-2 to 2.5×10^-2 m³. During the compression, 6 1×10³ J of work is done on the gas, and heat is removed to keep the temperature of the gas constant at all times. Calculate the temperature of the gas.

Answer 1

1.- For the first problem, we have to consider that the watermelon will lose heat while the cans of drinks will absorb that same heat, meaning that the sum of all heat should be equal to zero:

$Q_{12\,cans}+Q_{watermelon} =0 \,J$

$0 =(12\,cans)(0.35 \frac{kg}{can})(3800 \frac{J}{kg\,°C})(T_f-5°C)+(6.5kg)(4184 \frac{J}{kg\,°C})(T_f-27°C)$

$0 =(12)(0.35)(3800)(T_f-5°C)+(6.5)(4184)(T_f-27°C)$

$(15960\frac{J}{°C})(T_f-5°C)+(92196\frac{J}{°C})(T_f-27°C)=(108156 \frac{J}{°C})T_f-(2569092\,J)=0$

$\implies T_f=(2569092\,J)/(108156 \frac{J}{°C})=23.75\,°C$

After substitution, we find that the final temperature of the drinks and the watermelon will be 23.75 °C.

2.- For the second problem, we confirm that for an ideal gas the work done under constant pressure will be equal to -6.1 X 10³ J because the work is done to the gas:

$W_{A→B}=∫_{V_A}^{V_B} pdV=∫_{V_A}^{V_B} \frac{nRT}{V} dV = nRT\ln{\frac{V_B}{V_A}}$

From here we find that

$T=\large{\frac{W_{A→B}}{nR\ln{\frac{V_B}{V_A}}}}=\large{\frac{-6.1\times10^3\,J}{(3\,mol)(8.314\,J/molK)\ln{(\frac{2.5\times10^{-2}m³}{5.5\times10^{-2}m³}})}}$

$T=\large{\frac{6100}{19.6657}K}=310.18\,K$

In conclusion, the temperature of the gas while going under this process is equal to 310.18 K or 37.03 °C.

Reference:

• Atkins, P., & De Paula, J. (2011). Physical chemistry for the life sciences. Oxford University Press, USA.