# Tutor profile: Divya T.

## Questions

### Subject: Physics (Thermodynamics)

A steel ball of mass 1 kg of specific heat 0.4kJ/KgK is at a temperature of $$60^{o}C$$. It is dropped into 1 Kg water at $$20^{o}C$$. What is the final steady state temperature of the water?

Given data : Mass of steel ball $$m_{s}$$ = 1 kg. specific heat of ball = $$c_{s}$$ = 0.4kj/kgK Initial temperature of ball = $$T_{1}$$ = $$60^{o}C$$ Mass of water $$m_{w}$$ = 1 kg Initial temperature of water = $$T_{w1}$$ = $$20^{o}C$$ Let $$T_{f}$$ = final temperature of ball and water. Applying energy balance equation, Heat lost by steel ball = Heat gained by water. $$m_{s}$$$$c_{s}$$$$(T_{1}$$-$$T_{f})$$=$$m_{w}$$$$c_{w}$$$$(T_{f}$$-$$T_{w})$$ $$1*0.4(60-$$$$T_{f})$$=$$1*4.18$$$$(T_{f}-$$$$20)$$ 107.6 = 4.58$$T_{f}$$ $$T_{f}$$ = $$23.5^{o}C$$

### Subject: Physics (Heat Transfer)

For a current carrying wire of 20 mm diameter exposed to air (h= 20W/m^2K). The thermal conductivity of insulation in 0.5W/mK. What is the thickness of insulation at which maximum heat dissipation occurs?

We have, d = 20 mm r= d/2 = 20/2 = 10 mm k = 0.5W/mk h = 20W/m^2K For maximum heat dissipation, Critical radius = k/h for cylinder or wire. = 0.5/20 = 0.025 m = 25 mm Thickness of insulation = critical radius - radius of wire = (25-10) mm = 15 mm

### Subject: Basic Math

Adam is thrice as old as her youngest sister. If the difference between their ages is 10 years. How old is her youngest sister?

It's a very simple problem. Let's solve it: Let us assume that the age of Adam be 'x' years And, Age of his sister be 'y' years. As per the given condition, Adam's age = 3*(His sister's age) or, x = 3y This is equation (1) Now, (Adam's age) - (His sister's age) = 10 or, x - y = 10 This is equation (2) Putting x= 3y from (1) in (2), we get, 3y-y = 10 2y = 10 y= 5years = Age of Adam's sister From (1) x = 3y = 3*5 = 15years = Adam's age

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