Question

What is the pressure inside a 0.300cm³ box containing 400mol of Ar atoms, at 40^oC?

A 70 kg metal block with a specific heat capacity of 385 J/kgK is placed into 30 kg of water (specific heat capacity = 4180 J/kgK). The metal block was originally at 50^oC and the water was originally at 10^oC. What is the final temperature in Celsius for both?

Answer 1

The ideal gas equation is given by:

P*V=n*R*T;

p-pressure,v-volume ,t-temprature,n-no. of moles;

so using given data we have

P*(3*10^-7)=400*8.314*313; (temprature is written in kelvin and volume in m^3)

so P=3.47*10^12 pascal.

so pressure inside the box is  3.47*10^12 pascal.

Now;

mass of metal block=m1=70 kg;

specific heat =c1=385 j/kgk,

mass of water =m2=30kg;

heat capacity of water =c2=4180J/kgk;

initial temprature of block T1=50 degree=(273+50)kelvin=323 kelvin;

initial temprature of water T2=(273+10)=283 kelvin;;

now the heat lost by higher temprature body i.e. block will be gained by water ;

let T3 and T4are the final temprature of block and water respectively;

since at equlibirium both block and water will be at the same temprature so T3=T4;

heat transfered =mass*specific heat*change in temprature;

so we have m1*c1*(T1-T3)=m2*c2*(T3-T2)

70*385*(323-T3)=30*4180*(T3-283);

so 44,193,050=152,350 *T3;

T3=290.07 KELVIN

SO T3=290.17-273 degree=17.07 degree.

so final temprature of water and block is 17.07 degree celcius.