A tumbler, made purely of iron, can be filled with 500 ml (∼500cm3) of water during a spring temperature of 20∘C. How much water (in volume) can you store in the tumbler in autumn, if the temperature drops to 8∘C? (γFe = 33.3/∘C).
A tumbler, made purely of iron, can be filled with 500 ml (∼500cm3) of water during a spring temperature of 20∘C. How much water (in volume) can you store in the tumbler in autumn, if the temperature drops to 8∘C? (γFe = 33.3/∘C).
The correct option is A 499.8 mL
At 20∘C, the iron tumbler has a capacity of 500 cm3. When it gets colder during autumn, the tumbler will contract a little bit, and the exact capacity will reduce.
Here, ΔT = Tautumn - Tspring = 8∘C - 20∘C = −12∘C.
Also, γFe = 33.3 × 10−6/∘C
∴Vautumn = Vspring(1+γFe×ΔT)
= 500[1 + 33.3 × 10−6 × (−12)]cm3
= 499.8 cm3.
The tumbler's capacity will reduce only by 0.2cm3, or 0.2 mL, which is a real but hardly noticeable change. The reason that we don't notice significant shrinkage of objects around us in the winters is because the coefficients of expansion for most things are very small numbers, generally of the order of 10−6.
499.8 mL
At 20∘C, the iron tumbler has a capacity of 500 cm3. When it gets colder during autumn, the tumbler will contract a little bit, and the exact capacity will reduce.
Here, ΔT = Tautumn - Tspring = 8∘C - 20∘C = −12∘C.
Also, γFe = 33.3 × 10−6/∘C
∴Vautumn = Vspring(1+γFe×ΔT)
= 500[1 + 33.3 × 10−6 × (−12)]cm3
= 499.8 cm3.
The tumbler's capacity will reduce only by 0.2cm3, or 0.2 mL, which is a real but hardly noticeable change. The reason that we don't notice significant shrinkage of objects around us in the winters is because the coefficients of expansion for most things are very small numbers, generally of the order of 10−6.
