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Orlov [11]
3 years ago
11

How long does it take to raise the temperature of the air in a good-sized living room (3.00m×5.00m×8.00m) by 10.0∘C? Note that t

he specific heat of air is 1006 J/(kg⋅∘C) and the density of air is 1.20kg/m3.
Express your answer numerically in minutes, to three significant figures.
Physics
1 answer:
tekilochka [14]3 years ago
5 0

Answer : The time required is, 16.1 minutes.

Explanation :

First we have to calculate the amount of heat required to increase the temperature is:

Q=mC\Delta T\\\\Q=\rho VC\Delta T

(m=\rho V)

where,

Q = amount of heat required = ?

m = mass

\rho = density of air = 1.20kg/m^3

V = volume of air

C = specific heat of air = 1006J/kg^oC

\Delta T = change in temperature = 10.0^oC

Now put all the given values in above formula, we get:

Q=\rho VC\Delta T

Q=(1.20kg/m^3)\times (3.00m\times 5.00m\times 8.00m)\times (1006J/kg^oC)\times (10.0^oC)

Q=1.449\times 10^6J

Now we have to calculate the time required.

Formula used :

t=\frac{Q}{P}

where,

t = time required = ?

Q = amount of heat required = 1.449\times 10^6J

P = power = 1500 W

Now put all the given values in above formula, we get:

t=\frac{1.449\times 10^6J}{1500W}

t=966s\times \frac{1min}{60s}=16.1min

Thus, the time required is, 16.1 minutes.

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Answer:

Resistance of resistor A = 6.0 Ω and resistance of resistor B = 3.0 Ω

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When the two resistors are in series, let V₁ = voltage in resistor A and R₁ = resistance of resistor A and V₂ = voltage in resistor B and R₂ = resistance of resistor B.

Given that V₁ + V₂ = 6.0 V and V₁ = 4.0 V,

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equating both expressions, we have

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dividing through by 2.0 V, we have

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taking the reciprocal, we have

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R₁ = 2R₂

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The rotor in a certain electric motor is a flat, rectangular coil with 84 turns of wire and dimensions 2.61 cm by 3.64 cm. The r
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Given Information:

Number of turns = N = 84

Area of Rectangular coil = 2.61x3.64 cm = 0.0261x0.0364 m

Magnetic field = B = 0.80 T

Current = I = 10.5 mA = 0.0105 A

Angular speed = ω = 3.54x10³ rev/min

Required Information:

(a) Maximum torque = τmax = ?

(b) Peak output power = Ppeak = ?

(c) Work done = W = ?

(d) Average power = Pavg?

Answer:

(a) Maximum torque = 0.00067 N.m

(b) Peak output power = 0.248 W

(c) Work done = 0.00189 J

(d) Average power = 0.1115 W

Explanation:

(a) The toque τ acting on the rotor is given by,

τ = NIABsin(θ)

Where N is the number of turns, I is the current, A is the area of rectangular coil and B is the magnetic field

A = 0.0261x0.0364

A = 0.00095 m²

The maximum toque τ is achieved when θ = 90°

τmax = NIABsin(90°)

τmax = 84*0.0105*0.00095*0.80*1

τmax = 0.00067 N.m

(b) The peak output power of the motor is given by,

Pmax = τmax*ω

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(c) The amount of work done by the magnetic field on the rotor in every full revolution is given by

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W = -2NIABcos(ωt)

Evaluating limits,

W = -2NIABcos(π) - (-2NIABcos(0))

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t = 0.01694 sec

Pavg = W/t

Pavg = 0.00189/0.01694

Pavg = 0.1115 W

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3 years ago
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