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Dominik [7]
3 years ago
13

The heating element of a water heater in an apartment building has a maximum power output of 37 kW. Four residents of the buildi

ng take showers at the same time, and each receives heated water at a volume flow rate of 11x10-5 m3/s. If the water going into the heater has a temperature of 14°C, what is the maximum possible temperature of the hot water that each showering resident receives
Physics
1 answer:
kkurt [141]3 years ago
3 0

Answer:

maximum possible temperature is 34.088°C

Explanation:

Given data

power output Q = 37 kW

volume flow rate = 11 x 10^-5 m3/s

temperature t = 14°C

to find out

maximum possible temperature T

solution

we can say

total water volume  = 4 residents  × volume flow

total water volume = 4 × 11 x 10^-5  = 44 × 10^-5 m³/s

so we say total water mass = 1000 × volume

total water mass = 1000 kg/m³ ×  44 × 10^-5  

total water mass = 0.44 kg

we know

dQ/dt = (dm/dt)× (S)× ( T - t)

so here we know specific heat of water S = 4.186 joule/gram °C

37 = 0.44 × 4.186 × (T-14)

T = 34.088°C

maximum possible temperature is 34.088°C

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PART ONE
stira [4]

Answer:

3.64×10⁸ m

3.34×10⁻³ m/s²

Explanation:

Let's define some variables:

M₁ = mass of the Earth

r₁ = r = distance from the Earth's center

M₂ = mass of the moon

r₂ = d − r = distance from the moon's center

d = distance between the Earth and the moon

When the gravitational fields become equal:

GM₁m / r₁² = GM₂m / r₂²

M₁ / r₁² = M₂ / r₂²

M₁ / r² = M₂ / (d − r)²

M₁ / r² = M₂ / (d² − 2dr + r²)

M₁ (d² − 2dr + r²) = M₂ r²

M₁d² − 2dM₁ r + M₁ r² = M₂ r²

M₁d² − 2dM₁ r + (M₁ − M₂) r² = 0

d² − 2d r + (1 − M₂/M₁) r² = 0

Solving with quadratic formula:

r = [ 2d ± √(4d² − 4 (1 − M₂/M₁) d²) ] / 2 (1 − M₂/M₁)

r = [ 2d ± 2d√(1 − (1 − M₂/M₁)) ] / 2 (1 − M₂/M₁)

r = [ 2d ± 2d√(1 − 1 + M₂/M₁) ] / 2 (1 − M₂/M₁)

r = [ 2d ± 2d√(M₂/M₁) ] / 2 (1 − M₂/M₁)

When we plug in the values, we get:

r = 3.64×10⁸ m

If the moon wasn't there, the acceleration due to Earth's gravity would be:

g = GM / r²

g = (6.672×10⁻¹¹ N m²/kg²) (5.98×10²⁴ kg) / (3.64×10⁸ m)²

g = 3.34×10⁻³ m/s²

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3 years ago
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