Prove that when 'x' grams of steam at 100°C is mixed with 'y' grams of ice at 0°C and allowed to attain thermal equilibrium, the final temperature of mixture is 

Explanation:

Heat lost by the steam equals heat gained by the ice.

The steam first condenses, then cools.  The amount of heat lost is:

q = x Lvapor + x C (100 − T)

q = 2254x + 4.18x (100 − T)

The ice first melts, then warms.  The amount of heat gained is:

q = y Lfreeze + y C (T − 0)

q = 334y + 4.18y T

Setting the expressions equal:

2254x + 4.18x (100 − T) = 334y + 4.18y T

2254x + 418x − 4.184x T = 334y + 4.18y T

2672x − 334y = 4.18x T + 4.18y T

334 (8x − y) = 4.18 T (x + y)

T = 80 (8x − y) / (x + y)

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.