Question
It was a bright and breezy day in New York, the air was a cool 20 degrees Celsius, when Tony Stark, a.k.a the Iron Man's day took a dramatic turn as he got news of Mandarin's attack in the windy city of Chicago, and decided to immediately fly over there, in his iron body-armor, whose cavity had enough space to fit a man of 4,984 cm3 in volume, but not more.
Being a smart man, he did a quick check of two important things - his own body volume, which he found was currently 4.980 cm3, and the temperature in Chicago, which was a cold 8 degrees Celsius that day. Knowing that the coefficient of volume expansion for iron, γ, is 33.3 × 10−6/∘C, he decided to go. Check if that was a smart decision, by finding out whether the new volume of the iron suit when he reaches Chicago will crush him or not.
Being a smart man, he did a quick check of two important things - his own body volume, which he found was currently 4.980 cm3, and the temperature in Chicago, which was a cold 8 degrees Celsius that day. Knowing that the coefficient of volume expansion for iron, γ, is 33.3 × 10−6/∘C, he decided to go. Check if that was a smart decision, by finding out whether the new volume of the iron suit when he reaches Chicago will crush him or not.
Answer: Option A
:
A
Mr. Stark's suit is made of iron, which should contract upon cooling with a coefficient γ = 33.3×10−6/∘C. As he flies from New York to Chicago, there occurs a temperature drop of 12∘C.
∴ΔT = TChicago - TNY = (8∘C- 20∘C) = −12∘C
The volume, VNY, of the suit's cavity in New York = 4,984cm3.
∴ The volume of the cavity in Chicago will be -
VChicago = VNY(1+γΔT)
= 4.984[1+33.3×10−6×(−12)]cm3
≈ 4.982cm3.
Awesome! The suit will still fit Tony Stark comfortably in Chicago, so he can just concentrate on Mandarin's onslaught. I feel much less worried about Chicago now!
Was this answer helpful ?
:
A
Mr. Stark's suit is made of iron, which should contract upon cooling with a coefficient γ = 33.3×10−6/∘C. As he flies from New York to Chicago, there occurs a temperature drop of 12∘C.
∴ΔT = TChicago - TNY = (8∘C- 20∘C) = −12∘C
The volume, VNY, of the suit's cavity in New York = 4,984cm3.
∴ The volume of the cavity in Chicago will be -
VChicago = VNY(1+γΔT)
= 4.984[1+33.3×10−6×(−12)]cm3
≈ 4.982cm3.
Awesome! The suit will still fit Tony Stark comfortably in Chicago, so he can just concentrate on Mandarin's onslaught. I feel much less worried about Chicago now!
Was this answer helpful ?
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