Home
Class 11
PHYSICS
A gasoline tank made of steel is filled ...

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)`

Text Solution

Verified by Experts

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
Promotional Banner

Topper's Solved these Questions

  • THERMAL PROPERTIES OF MATTER

    MODERN PUBLICATION|Exercise PRACTICE PROBLEM|28 Videos

  • THERMAL PROPERTIES OF MATTER

    MODERN PUBLICATION|Exercise CONCEPTUAL QUESTIONS|16 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    MODERN PUBLICATION|Exercise Chapter Practice Test (for Board Examination)|16 Videos

  • UNITS AND MEASUREMENT

    MODERN PUBLICATION|Exercise CHAPTER PRACTICE TEST|15 Videos

Similar Questions

Explore conceptually related problems

Assume that one early morning when the temperature is 10^(@)C a driver of an automobile gets his gasoline tank which is made of steel, filled with 75 L of gasoline, which is also at 10^(@)C Durign the day, the temperature rises at 30^(@)C how much gasoline will overflow ? (Given, alpha for steel = 1.2 xx 10^(-5)"^(@) C^(-1),gamma for gasoline = 9.5 xx 10^(-4)"^(@)C)

Assume that one early morning when the temperatures in 10^(@)C, a driver of an automobile gets his gasoline tank which is made of steel, tilled with 75 L of gasoline, which is also at 10^(@)C. During the day, the tempaerature rises to 30^(@)C, how much gasoline will overflow ? (Given, alpha for steel =1.2xx 10^(-5)"^(@)C^(^1), gamma for gasoline =9.5xx10^(-4)"^(@)C^(-1))

A second's pendulum clock has a steel wire. The clock is calibrated at 20^@ C . How much time does the clock lose or gain in one week when the temperature is increased to 30^@ C ? alpha_(steel = 1.2 xx 10^-5(^@ C)^-1 .

The driver of an automobile gets his steel gasoline tank filled with 50 ltrs of gasoline at surrounding temperature of 20^@C . At afternoon, the temperature rises to 40^@C . How much of the gasoline will overflow? Coefficient of linear expansion for steel , alpha_s = 1.3 xx 10^(-5) ""^@C^(-1) and for gasoline gamma_g = 9.4 xx 10^(-4) ""^@C^(-1)

An iron sphere has a radius of 10 cm at a temperature of 0^(@)C . Calculate the change in volume of the sphere if it is heated to 100^(@)C . Given alpha_(Fe) = 1.1 xx 10^(-6).^(@)C^(-1)

A surveryor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20^(@)C What is its length on a hot summer day when the temperature is 35^(@)C ? (alpha_("stell")=1.2xx10^(-5)K^(-1))

A wire of cross sectional area 3 mm^(2) is just stretched between two fixed points at a temperature of 20^(@)C . Then the tension in the wire when the temperature falls to 10^(@)C is, (alpha =1.2 xx 10^(-5) //""^(@)C, Y=2xx10^(11) N//m^(2))

The scale on a steel on a steel meter stick is calibrated at 15^@ C . What is the error in the reading of 60 cm at 27^@C ? alpha_(steel) =1.2 xx 10^-5 (.^@ C)^-1 .

Two fines steel wires , fastened between the projectors of a heavy brass bar, are just taut when the whole system is at 0^(@)C . What is the tensile stress in the steel wires the temperature of the system is raised by 200^(@)C ? ( alpha_("glass") = 2 xx 10^(-5) ^(@)C ^(-1), alpha_("steel") = 1.2 xx 10^(-5)"^(@)C^(-1), Y_("steel") = 200GNm^(-2) )

A glass flask of volume 200cm^(3) is just filled with mercury at 20^(@)C . The amount of mercury that will overflow when the temperature of the system is raised to 100^(@)C is (gamma_(glass)=1.2xx10^(-5)//C^(@),gamma_(mercury)=1.8xx10^(-4)//C^(@))