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 $c m^{3}$ 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 $c m^{3}$ , 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 $33.3 \times 10^{- 6}$ $/^{\circ} C$ , 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.

4.982 c m^{3}

(he is going to be alright)

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4.979 c m^{3}

(it's going to be an uncomfortable encounter)

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4.938 c m^{3}

(he will have to take his suit off and call the Hulk)

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4.980 c m^{3}

(perfect fit!).

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Solution

The correct option is A $4.982 c m^{3}$ (he is going to be alright)
Mr. Stark's suit is made of iron, which should contract upon cooling with a coefficient $γ$ = $33.3 \times 10^{- 6}$ $/^{\circ} C$ . As he flies from New York to Chicago, there occurs a temperature drop of $12^{\circ} C$ .

$∴$ $Δ T$ = $T_{C h i c a g o}$ - $T_{N Y}$ = ( $8^{\circ} C$ - $20^{\circ} C$ ) = $- 12^{\circ} C$

The volume, $V_{N Y}$ , of the suit's cavity in New York = $4, 984 c m^{3}$ .

$∴$ The volume of the cavity in Chicago will be -

$V_{C h i c a g o}$ = $V_{N Y} (1 + γ Δ T)$

= $4.984 [1 + 33.3 \times 10^{- 6} \times (- 12)] c m^{3}$

$\approx$ $4.982 c m^{3}$ .

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!

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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 $c m^{3}$ in volume, but not more.

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