CBSE

Class 12

Physics

Magnetism, EMI and AC

A resistance coil of resistance r connected to an external bat

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A resistance coil of resistance r connected to an external battery, is placed inside an adiabatic cylinder fitted with a frictionless platon of mass m and same area A. Initially cylinder contains one mole of ideal gas he. A current through the coil such that temperature of gas varies as $T = T_{0} + at + bt^{2},$ keeping pressure constant with time t. Atosphere pressure above piston is $P_{0}$ . Find

(a) Current l flowing through the coil as function of time and
(b) Speed of piston as function of time.

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Text solutionVerified

Sure, here are the step by step solutions: 1. Heat produced by coil inside the cylinder in time dt is

d Q = l^{2} r d t \dots (i)

2. As we know,

d Q = n C_{P} d T

I^{2} r d t = \frac{5 R}{2} d T \dots (C_{P} = \frac{5 R}{2})

3. Here,

T = T_{0} + a t + b t^{2}

\frac{d T}{d t} = a + 2 b t

4. From equation (ii), we get

I = \frac{5 R}{2 r} (2 b t + a)

5. Since pressure is constant, we have

P V = RT \Rightarrow P d V = R d T

P A d x = R d T

6. The velocity is given by

v = \frac{d x}{d t} = \frac{R}{P A}

\frac{d T}{d t} = \frac{R}{P A} (2 b t + a) \dots (where P_{0} A + m g = P A)

\frac{d T}{d t} = \frac{R}{P _{0} A + m g} (2 b t + a)

Thus, we have derived the solutions step by step.

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A resistance coil of resistance r connected to an external battery, is placed inside an adiabatic cylinder fitted with a frictionless platon of mass m and same area A. Initially cylinder contains one mole of ideal gas he. A current through the coil such that temperature of gas varies as

T = T_{0} + at + bt^{2},

keeping pressure constant with time t. Atosphere pressure above piston is

P_{0}

. Find

(a) Current l flowing through the coil as function of time and
(b) Speed of piston as function of time.

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Question Text	A resistance coil of resistance r connected to an external battery, is placed inside an adiabatic cylinder fitted with a frictionless platon of mass m and same area A. Initially cylinder contains one mole of ideal gas he. A current through the coil such that temperature of gas varies as $T = T_{0} + at + bt^{2},$ keeping pressure constant with time t. Atosphere pressure above piston is $P_{0}$ . Find (a) Current l flowing through the coil as function of time and (b) Speed of piston as function of time.
Topic	Magnetism, EMI and AC
Subject	Physics
Class	Class 12
Answer Type	Text solution:1

Text solutionVerified

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