The densities of wood and benzene at 0^C are 880 kg m^3 and 900 kg m^(-3) respectively. The coefficients of volume expansion are 1.2 xx10^(-3) 0^C(-1) for wood and 1.5 xx 10^(-3) 0^C(-1) for benzene. At temperature will a piece of wood just sink in benzene?

The densities of wood and benzene at 0^C are 880 kg m^3 and 900 kg m^(

1.	The densities of wood and benzene at 0^C are 880 kg m^3 and 900 kg m^(-3) respectively. The coefficients of volume expansion are 1.2 xx10^(-3) 0^C(-1) for wood and 1.5 xx 10^(-3) 0^C(-1) for benzene. At temperature will a piece of wood just sink in benzene?
Answer» Solution :Given `f_w = 880 kg/m^3,` ` f_b= 900kg/m^3` `T_1=0^@C,` `gamma_w = 1.2 xx 10^-3/^@C,` ` gamma_b = (1.5 xx 10^-3/^@C)` The sphere begins to sink when ` rArr (mg)_sphere = displaced water ` ` (Vf'_w)G = (Vf'_b)g` ` rArrf_w /(1+(gamma_w) Delta THETA)= f_b/(1+(gamma_b) Delta theta)` ` rArr (880/(1+1.2 xx (10^-3) Delta theta))= (900/ ( 1+1.5 xx (10^-3) Delta theta))` ` rArr (880+880 xx 1.5 xx (10^-3) Delta theta )` ` (900+900 xx 1.2 xx (10^-3) Delta theta)` `rArr (880 xx 1.5 xx (10^-3)- 900 xx 1.2 xx (10^-3))Delta theta` ` =20` ` rArr (1320-1080) xx (10^-3)Delta theta = 20` ` rArrDelta theta = 83.3^@C` ` T_2- T_1 = 83rArrT_2- 0^@C= 83` ` rArr T_2 = 83^@C`