Question

A 500 g chunk of solid mercury at its 234 K melting point is added to 1500 g of liquid mercury at room temp (293 K). Determine the equilibrium mix and temperature.

How much power does it take to raise the temperature of a 1.3 kg copper pipe by 15 oC/s? Relate this to the time you spend waiting for your shower to warm up. One inch copper pipe is .837 lb/foot. Assume that your shower is 30 feet from the hot water heater and the flow rate is 12 l/min.

In a lab exercise simulating James Joule’s famous experiment, 1.0 kg of water, in a perfectly insulated container is stirred vigorously until its temperature rises by 7.0oC. How much work was done on the water?

A monatomic gas is adiabatically compressed to 1/8 of its original volume. Do each of the following quantities change? If so, does the quantity increase or decrease, and by what factor? If not, why not?

a. The rms speed vrms.

b. The thermal energy of the gas.

c. The molar specific heat CV

Please help with whatever question you can

Answer 1

(1) Mass of solid mercury (M) = 500g
Mass of the liquid mercury (m) = 1500 g
temperature ot the liquid mercury (T_Li) = 293 K
Specific heat of mercury (C) = 0.140 J/gmK
Latent heat of melting of mercury (L_M) = 11.3 J/g
Now energy available with liquid mercury = mC*(T_Li - T_m) + mL_m
(E_A)= 1500*(0.14)*(293 -234) + 1500*11.3 = 29340 J
Now we have total solid mercury(M_T) = M+ m = 500 + 1500 = 2000 g
Energy required to convert this sold mercury into liquid
E₁ = M_T*L_M = 2000*11.3 = 22600 J
Since the availabel energy is more than the required therfore total mass will convert into liquid.
now energy remains ater conversion in to solid (E_R) = E_A - E₁ = 29340 - 22600 = 6740 J
Now the temperature raised will be
M_T*C*(T -T_m) = 6740
2000*0.14*(T-234) = 6740
T = 258.07 K
hence the final temperature of the mixture will be 258.07 K