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DochEvi [55]
1 year ago
10

A 248-g piece of copper is dropped into 390 mL of water at 22.6 °C. The final temperature of the water was measured as 39.9 °C.

Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water. Remember, the density of water is 1.0 g/m
Physics
1 answer:
Sedaia [141]1 year ago
7 0

Answer:

335°C

Explanation:

Heat gained or lost is:

q = m C ΔT

where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

Heat gained by the water = heat lost by the copper

mw Cw ΔTw = mc Cc ΔTc

The water and copper reach the same final temperature, so:

mw Cw (T - Tw) = mc Cc (Tc - T)

Given:

mw = 390 g

Cw = 4.186 J/g/°C

Tw = 22.6°C

mc = 248 g

Cc = 0.386 J/g/°C

T = 39.9°C

Find: Tc

(390) (4.186) (39.9 - 22.6) = (248) (0.386) (Tc - 39.9)

Tc = 335

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Two resistors of resistances R1 and R2, with R2&gt;R1, are connected to a voltage source with voltage V0. When the resistors are
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Answer

The Value of  r  = 0.127

Explanation:

The mathematical representation of the two resistors connected in series is

                               R_T = R_1 +R_2

 And from Ohm law

                           I_s =\frac{ V}{R_T}

                            I_s  = \frac{V_0}{R_1 +R_2} ---(1)

The mathematical representation of the two resistors connected in parallel  is

                    R_T = \frac{1}{R_1} +\frac{1}{R_2}

                          = \frac{R_1 R_2}{R_1 +R_2}

From the question I_p =10I_s

          =>                 I_p =10I_s = \frac{V_0 }{\frac{R_1R_2}{R_1 +R_2} }  = \frac{V_0 (R_1 +R_2)}{R_1 R_2}---(2)

     Dividing equation 2 with equation 1

       =>                 \frac{10I_s}{I_s} =\frac{\frac{V_0 (R_1 +R_2)}{R_1 R_2}}{\frac{V_0}{R_1 +R_2}}

                                  10 = \frac{(R_1+R_2)^2}{R_1 R_2}----(3)

We are told that    r = \frac{R_1}{R_2} \ \ \ \ \  = > R_1 = rR_2

From equation 3  

                            10 = \frac{(1-r)^2}{r}

=> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  1+r^2 + 2r = 10r

=> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r^2 -8r+1 = 0

Using the quadratic formula

                             r =\frac{-b\pm \sqrt{(b^2 - 4ac)} }{2a}

        a = 1  b = -8 c =1  

                              =  \frac{8 \pm\sqrt{((-8)^2- (4*1*1))} }{2*1}

                               r= \frac{8+ \sqrt{60} }{2}  \ or \  r = \frac{8 - \sqrt{60} }{2}

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Now  r =  0.127 because it is the least value among the obtained values

                               

                                   

                             

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