A gasoline tank made of steel is filled completely with 60 litres of gasoline, both at a temperature of 12^@C . How much gasoline will overflow when the temperature is increased to 25^@C ? alpha_("steel") = 1.1 xx 10^(-5) ""^@C^(-1) gamma_("gasoline") = 9.5 xx 10^(-4) ""^@C^(-1)

A gasoline tank made of steel is filled completely with 60 litres of g

1.	A gasoline tank made of steel is filled completely with 60 litres of gasoline, both at a temperature of 12^@C . How much gasoline will overflow when the temperature is increased to 25^@C ? alpha_("steel") = 1.1 xx 10^(-5) ""^@C^(-1) gamma_("gasoline") = 9.5 xx 10^(-4) ""^@C^(-1)
Answer» Solution :Volume of gasoline = Volume of steel tank, V = 60l `Delta T = 15 - 12 = 13^@C` ` gamma_("gasoline") = 9.5 xx 10^(-4) ""^@C^(-1)` Change in volume of gasoline is `DeltaV_(g) = gamma_("gasoline") V Delta T` ` = 9.6 xx 10^(-4) xx 60 xx 3` Change in volume of steel tank, ` Delta V_s= gamma_("steel") V Delta T` ` = 3 alpha_("steel") V Delta T` ` = 3 xx 1.1 xx 10^(-5) xx 60 xx 13` Volume of gasoline that overflows is ` Delta V_g- Delta V_s = 9.5 xx 10^(-4) xx 60 xx 13 -3 xx 1.1 xx 10^(-5) xx 60 xx 13` ` = (9.5 xx 10^(-4) - 3 xx 1.1 xx 10^(-5) ) xx 60 xx 13` ` = (9.5- 0.33) xx 10^(-4) xx 60 xx 13` `= 9.17 xx 60 xx 13 xx 10^(-4) ` = 0.715 litres