Which of the following occurs during the evolution of a star?

You pour 250 g of tea into a Styrofoam cup, initially at 80∘C and stir in a little sugar using a 100-g aluminum 20∘C spoon and l

jok3333 [9.3K]

To solve this problem it is necessary to apply the concepts related to the conservation of energy and heat transferred in a body.

By definition we know that the heat lost must be equal to the heat gained, ie

$Q_g = Q_l$

Where,

Q = Heat exchange

The heat exchange is defined as

$Q = c_p m \Delta T$

Where,

$c_p =$ Specific heat

m = mass

$\Delta T=$ Change in Temperature

Therefore replacing we have that

$Q_g = Q_l$

$c_{p-tea} m \Delta T = c_{p-al} m \Delta T$

Replacing with our values we have that

$0.25*4180*(80-T) = 0.1*900*(T-20)$

$11.61*(80-T) = T-20$

$T= \frac{948.8}{11.61}$

$T = 75.24\°C$

Therefore the highest possible temperature of the spoon when you finally take it out of the cup is 75.24°C

3 0

3 years ago

State and prove bessel inequality

maria [59]

Statement :- We assume the orthagonal sequence ${{\{\phi\}}_{1}^{\infty}}$ in Hilbert space, now ${\forall \sf \:v\in \mathbb{V}}$ , the Fourier coefficients are given by:

${\quad \qquad \longrightarrow \sf a_{i}=(v,{\phi}_{i})}$

Then Bessel's inequality give us:

${\boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Proof :- We assume the following equation is true

${\quad \qquad \longrightarrow \displaystyle \sf v_{n}=\sum_{i=1}^{n}a_{i}{\phi}_{i}}$

So that, ${\bf v_n}$ is projection of ${\bf v}$ onto the surface by the first ${\bf n}$ of the ${\bf \phi_{i}}$ . For any event, ${\sf (v-v_{n})\perp v_{n}}$

Now, by Pythagoras theorem:

${:\implies \quad \sf \Vert v\Vert^{2}=\Vert v-v_{n}\Vert^{2}+\Vert v_{n}\Vert^{2}}$

${:\implies \quad \displaystyle \sf ||v||^{2}=\Vert v-v_{n}\Vert^{2}+\sum_{i=1}^{n}\vert a_{i}\vert^{2}}$

Now, we can deduce that from the above equation that;

${:\implies \quad \displaystyle \sf \sum_{i=1}^{n}\vert a_{i} \vert^{2}\leqslant \Vert v\Vert^{2}}$

For ${\sf n\to \infty}$ , we have

${:\implies \quad \boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Hence, Proved

5 0

2 years ago

Read 2 more answers

What evidence can you cite to support the claim that the frequency of light does not change upon reflection?

sergiy2304 [10]

Answer: The color of an image is identical to the color of the object forming the image. When you look at yourself in a mirror, the color of your eyes doesn’t change. The fact that the color is the same is evidence that the frequency of light doesn’t change upon reflection. 2.

Hope this helps!!

5 0

3 years ago

Imvu?<br> ..............................

Dominik [7]

Imvu? Like the app?

4 0

3 years ago

Read 2 more answers

The process of wind blowing sand from one location to another is called

lesya [120]

Answer: